Which does not describe the same situation?(1 point)Responsesy = 3x + 5y = 3 x + 5x –3 1 4y –4 8 17x –3 1 4 y –4 8 17graphImage with alt text: graphy is five more than three times x.
The third response does not describe the same situation.
What is an equation of the line in slope intercept form?m = 4 and the y-intercept is (0, 5)(1 point)Responsesy = 4x – 5y = 4 x – 5y = –5x +4y = –5 x +4y = 4x + 5y = 4 x + 5y = 5x +4
The equation of the line in slope-intercept form is y = 4x + 5.
Write the equation in slope-intercept form. What are the slope and y-intercept?–5x – 12y = 11(1 point)ResponsesEquationImage with alt text: EquationEquationImage with alt text: EquationEquationImage with alt text: EquationEquation
To write the equation in slope-intercept form, we need to solve for y.
-5x - 12y = 11
To isolate y, we can rearrange the equation:
-12y = 5x + 11
Dividing both sides by -12:
y = (-5/12)x - 11/12
The slope of the line is -5/12 and the y-intercept is -11/12.
Which graph best represents the equation x + 2y = 4?(1 point)ResponsesA line graphed on a coordinate plane passes through the points left parenthesis 0 comma 4 right parenthesis and left parenthesis 4 comma negative 4 right parenthesis.Image with alt text: A line graphed on a coordinate plane passes through the points left parenthesis 0 comma 4 right parenthesis and left parenthesis 4 comma negative 4 right parenthesis.A line graphed on a coordinate plane passes through the points left parenthesis negative 4 comma 3 right parenthesis and left parenthesis 4 comma negative 1 right parenthesis.Image with alt text: A line graphed on a coordinate plane passes through the points left parenthesis negative 4 comma 3 right parenthesis and left parenthesis 4 comma negative 1 right parenthesis.A line graphed on a coordinate plane passes through the points left parenthesis negative 4 comma 4 right parenthesis and left parenthesis 4 comma 0 right parenthesis.Image with alt text: A line graphed on a coordinate plane passes through the points left parenthesis negative 4 comma 4 right parenthesis and left parenthesis 4 comma 0 right parenthesis.A line graphed on a coordinate plane passes through the points left parenthesis negative 1 comma 4 right parenthesis and left parenthesis 3 comma negative 4 right parenthesis.Image with alt text: A line graphed on a coordinate plane passes through the points left parenthesis negative 1 comma 4 right parenthesis and left parenthesis 3 comma negative 4 right parenthesis.Skip to navigation
The correct response is:
A line graphed on a coordinate plane passes through the points (0, 4) and (4, -4).
The graph of a line is shown on a coordinate grid. The line connects the points left-parenthesis negative 2 comma negative 5 right-parenthesis and left-parenthesis 1 comma 4 right-parenthesis.Which equation best represents the line graphed above?(1 point)Responsesy = –3x – 1y = –3 x – 1y = –3x + 1y = –3 x + 1y = 3x + 1y = 3 x + 1y = 3x – 1
The equation that best represents the line graphed above is:
y = 3x - 1.
The graph of a line is shown on a coordinate grid. The line is parallel to the y-axis and passes through the point left-parenthesis negative 1 comma 0 right-parenthesis.Which equation best represents the line graphed above?(1 point)Responsesx = –1x = –1x = 1x = 1y = –1y = –1y = x – 1
The equation that best represents the line graphed above is:
x = -1.
The table below shows the time, in seconds, that it takes to fill 20-ounce bottles with water.Time (in seconds)Number of bottles filled003066012901812024Which graph best models the relationship in the table?(1 point)ResponsesA graph shows the number of bottles per second.The y-axis is labeled number of bottles and is labeled from 0 to 24 in increments of 6. The x-axis is labeled time in seconds and is labeled from 0 to 120 in increments of 30. The ray starts at left parenthesis 0 comma 0 right parenthesis and goes through left parenthesis 120 comma 24 right parenthesis.Image with alt text: A graph shows the number of bottles per second. The y-axis is labeled number of bottles and is labeled from 0 to 24 in increments of 6. The x-axis is labeled time in seconds and is labeled from 0 to 120 in increments of 30. The ray starts at left parenthesis 0 comma 0 right parenthesis and goes through left parenthesis 120 comma 24 right parenthesis.A graph shows the number of bottles per second.The y-axis is labeled number of bottles and is labeled from 0 to 24 in increments of 6. The x-axis is labeled time in seconds and is labeled from 0 to 120 in increments of 30. The ray starts at left parenthesis 0 comma 6 right parenthesis and goes through left parenthesis 90 comma 24 right parenthesis.Image with alt text: A graph shows the number of bottles per second. The y-axis is labeled number of bottles and is labeled from 0 to 24 in increments of 6. The x-axis is labeled time in seconds and is labeled from 0 to 120 in increments of 30. The ray starts at left parenthesis 0 comma 6 right parenthesis and goes through left parenthesis 90 comma 24 right parenthesis.A graph shows the number of bottles per second.The y-axis is labeled number of bottles and is labeled from 0 to 24 in increments of 6. The x-axis is labeled time in seconds and is labeled from 0 to 120 in increments of 30. The ray starts at left parenthesis 30 comma 0 right parenthesis and goes through left parenthesis 120 comma 18 right parenthesis.Image with alt text: A graph shows the number of bottles per second. The y-axis is labeled number of bottles and is labeled from 0 to 24 in increments of 6. The x-axis is labeled time in seconds and is labeled from 0 to 120 in increments of 30. The ray starts at left parenthesis 30 comma 0 right parenthesis and goes through left parenthesis 120 comma 18 right parenthesis.A graph shows the number of bottles per second.The y-axis is labeled number of bottles and is labeled from 0 to 120 in increments of 30. The x-axis is labeled time in seconds and is labeled from 0 to 24 in increments of 6. The ray starts at left parenthesis 0 comma 0 right parenthesis and goes through left parenthesis 24 comma 120 right parenthesis.Image with alt text: A graph shows the number of bottles per second. The y-axis is labeled number of bottles and is labeled from 0 to 120 in increments of 30. The x-axis is labeled time in seconds and is labeled from 0 to 24 in increments of 6. The ray starts at left parenthesis 0 comma 0 right parenthesis and goes through left parenthesis 24 comma 120 right parenthesis.Skip to navigation
The correct response is:
A graph shows the number of bottles per second.
The y-axis is labeled number of bottles and is labeled from 0 to 24 in increments of 6.
The x-axis is labeled time in seconds and is labeled from 0 to 120 in increments of 30.
The ray starts at (0, 6) and goes through (90, 24).
QuestionWhich procedure could be used to graph the following equation?y equals one-fourth x minus 1(1 point)ResponsesPlot the y-intercept (0, –1) and use the slope of one-fourth to find a second point.Plot the y -intercept (0, –1) and use the slope of Image with alt text: one-fourth to find a second point.Plot the y-intercept left parenthesis 0 comma one-fourth right parenthesis and use the slope of –1 to find a second point.Plot the y -intercept Image with alt text: left parenthesis 0 comma one-fourth right parenthesis and use the slope of –1 to find a second point.Plot the x-interceptleft parenthesis one-fourth comma 0 right parenthesis and use the slope of –1 to find a second point.Plot the x -intercept Image with alt text: left parenthesis one-fourth comma 0 right parenthesis and use the slope of –1 to find a second point.Plot the x-intercept (–1, 0) and use the slope of one-fourth to find a second point.Plot the x -intercept (–1, 0) and use the slope of Image with alt text: one-fourth to find a second point.Skip to navigation
The correct response is:
Plot the y-intercept (0, –1) and use the slope of one-fourth to find a second point.
Which equation defines the graph of y = x3 after it is shifted vertically 5 units down and horizontally 4 units left?(1 point)Responsesy = (x – 4)3 – 5y = ( x – 4) 3 – 5y = (x + 5)3 – 4y = ( x + 5) 3 – 4y = (x + 5)3 + 4y = ( x + 5) 3 + 4y = (x + 4)3 – 5
The equation that defines the graph of y = x^3 after it is shifted vertically 5 units down and horizontally 4 units left is:
y = (x + 4)^3 - 5.
The graph of y = x2 is shown below.The graph of a upward facing parabola is shown on a coordinate plane. The parabola has a vertex at left-parenthesis 0 comma 0 right-parenthesis and is symmetric over the y-axis. The parabola is labeled y equals x squared.If graphed on the same grid, which of the following could be the graph of y = 0.4x2?(1 point)ResponsesA coordinate plane. A parabola extends from quadrant 3 to quadrant 4 close to the y-axis with a point at 0 comma 0.Image with alt text: A coordinate plane. A parabola extends from quadrant 3 to quadrant 4 close to the y-axis with a point at 0 comma 0.A coordinate plane. A parabola extends from the middle of quadrant 2 to the middle of quadrant 1. A point is at 0 comma 0.Image with alt text: A coordinate plane. A parabola extends from the middle of quadrant 2 to the middle of quadrant 1. A point is at 0 comma 0.A coordinate plane. A parabola extends from quadrant 2 to quadrant 1 close to the y-axis. A point is at 0 comma 0.Image with alt text: A coordinate plane. A parabola extends from quadrant 2 to quadrant 1 close to the y-axis. A point is at 0 comma 0.A coordinate plane. A parabola extends from the middle of quadrant 3 to the middle of quadrant 4. A point is at 0 comma 0.Image with alt text: A coordinate plane. A parabola extends from the middle of quadrant 3 to the middle of quadrant 4. A point is at 0 comma 0.
The correct response is:
A coordinate plane. A parabola extends from the middle of quadrant 2 to the middle of quadrant 1. A point is at (0, 0).
A graph of a parabola is shown on a coordinate grid. The curve connects the points left-parenthesis negative 3 comma 0 right-parenthesis, left-parenthesis negative 1 comma negative 4 right-parenthesis, and left-parenthesis 1 comma 0 right-parenthesis.Which equation best represents the graph above?(1 point)Responsesy = (x + 1)² – 4y = ( x + 1)² – 4y = (x – 1)² – 4y = ( x – 1)² – 4y = (x + 1)²y = (x + 1)²y = (x – 1)²
The equation that best represents the graph above is:
y = (x + 1)² – 4.
Which of the following shows the graph of the inequality y > –x – 2?(1 point)ResponsesA dotted line graphed on a coordinate plane passes through the points left parenthesis negative 5 comma 3 right parenthesis and left parenthesis 3 comma negative 5 right parenthesis. The area above the line is shaded.Image with alt text: A dotted line graphed on a coordinate plane passes through the points left parenthesis negative 5 comma 3 right parenthesis and left parenthesis 3 comma negative 5 right parenthesis. The area above the line is shaded.A dotted line graphed on a coordinate plane passes through the points left parenthesis negative 5 comma 3 right parenthesis and left parenthesis 3 comma negative 5 right parenthesis. The area below the line is shaded.Image with alt text: A dotted line graphed on a coordinate plane passes through the points left parenthesis negative 5 comma 3 right parenthesis and left parenthesis 3 comma negative 5 right parenthesis. The area below the line is shaded.A dotted line graphed on a coordinate plane passes through the points left parenthesis negative 3 comma negative 5 right parenthesis and left parenthesis 5 comma 3 right parenthesis. The area above the line is shaded.Image with alt text: A dotted line graphed on a coordinate plane passes through the points left parenthesis negative 3 comma negative 5 right parenthesis and left parenthesis 5 comma 3 right parenthesis. The area above the line is shaded.A line graphed on a coordinate plane passes through the points left parenthesis negative 5 comma 3 right parenthesis and left parenthesis 3 comma negative 5 right parenthesis. The area above the line is shaded.Image with alt text: A line graphed on a coordinate plane passes through the points left parenthesis negative 5 comma 3 right parenthesis and left parenthesis 3 comma negative 5 right parenthesis. The area above the line is shaded.Skip to navigation
The correct response is:
A dotted line graphed on a coordinate plane passes through the points (-5, 3) and (3, -5). The area above the line is shaded.
A linear inequality is graphed on a coordinate plane. The solid line passes through the points left parenthesis negative 6 comma negative 7 right parenthesis, left parenthesis 0 comma 4 right parenthesis, and left parenthesis 8 comma 0 right parenthesis. The graph is shaded below the line.(1 point)Responsesy less-than-or-equal-to negative StartFraction 1 over 2 EndFraction x plus 4Image with alt text: y less-than-or-equal-to negative StartFraction 1 over 2 EndFraction x plus 4y less-than-or-equal-to 4 x minus StartFraction 1 over 2 EndFractionImage with alt text: y less-than-or-equal-to 4 x minus StartFraction 1 over 2 EndFractiony greater-than-or-equal-to negative StartFraction 1 over 2 EndFraction x plus 4Image with alt text: y greater-than-or-equal-to negative StartFraction 1 over 2 EndFraction x plus 4y less-than-or-equal-to StartFraction 1 over 2 EndFraction x plus 4
The correct response is:
y ≤ ½x + 4.
An electronics store makes a profit of $32 for every portable DVD player sold and $64 for every DVD recorder sold. The manager’s target is to make at least $256 a day on sales of the portable DVD players and DVD recorders. Write an inequality that represents the number of both kinds of DVD players that can be sold to reach or beat the sales target. Let p represent the number of portable DVD players and r represent the number of DVD recorders.(1 point)Responses32p + 64r ≥ 25632 p + 64 r ≥ 25664p + 32r ≥ 25664 p + 32 r ≥ 25632p + 64r > 25632 p + 64 r > 25632p + 64r < 256
The correct response is:
32p + 64r ≥ 256.