Graphing Linear Equations Unit Test
8 of 158 of 15 Items
Question
Use the image to answer the question.
An illustration shows two graphs depicting earnings per hour for employees 1 and 2. The first graph shows earnings per hour for employee 1. The horizontal axis shows hours ranging from 0 to 8 in increments of 2. The vertical axis shows earnings in dollars ranging from 0 to 80 in increments of 5. Four data points are plotted on the graph at left parenthesis 0 comma 0 right parenthesis, left parenthesis 2 comma 25 right parenthesis, left parenthesis 4 comma 50 right parenthesis, and left parenthesis 6 comma 75 right parenthesis. A line connects all the data points. The second graph shows earnings per hour for employee 2. The horizontal axis shows hours ranging from 0 to 6 in increments of 1. The vertical axis shows earnings in dollars ranging from 0 to 80 in increments of 5. Four data points are plotted on the graph at left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 15 right parenthesis, left parenthesis 3 comma 45 right parenthesis, and left parenthesis 5 comma 75 right parenthesis. A line connects all the data points.
The earnings for Employee 1 and Employee 2 are displayed in the following graphs. Which employee earns more per hour?
(1 point)
Employee
earns more per hour.
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Employee 1 earns more per hour.
Graphing Linear Equations Unit Test
9 of 159 of 15 Items
Question
Use the image to answer the question.
An illustration shows a coordinate plane with the x-axis ranging from negative 9 to 9 in one unit increments, and the y-axis ranging from negative 11 to 11 in one unit increments. A solid line passes through four plotted points and extends beyond. A solid line with arrows at both ends passes through points with coordinates left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 3 right parenthesis, left parenthesis 2 comma 6 right parenthesis, and left parenthesis 3 comma 9 right parenthesis. The solid line forms the hypotenuse for two triangles. The first triangle is marked with a dotted line and has vertices with coordinates left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 0 right parenthesis, and left parenthesis 1 comma 3 right parenthesis. The base is labeled as 1, and the perpendicular height on the right is labeled as 3. The second triangle is marked with a dashed line and has vertices with coordinates left parenthesis 1 comma 3 right parenthesis, left parenthesis 3 comma 3 right parenthesis, and left parenthesis 3 comma 9 right parenthesis. The base is labeled as 2, and the perpendicular height on the right is labeled as 6.
Use similar triangles to determine the slope of the line.
(1 point)
The slope is
3
Graphing Linear Equations Unit Test
10 of 1510 of 15 Items
Question
Use the table to answer the question.
($) Cost of Candy Bar A
Quantity ($) Cost
1 1.25
2 2.50
3 3.75
4 5.00
5 6.25
The cost of Candy Bar A is displayed in the table. The proportional relationship between the cost and quantity for Candy Bar B is represented by the equation y=x . Which candy bar is the cheapest cost per bar? Enter 1 for Candy Bar A. Enter 2 for Candy Bar B.
(1 point)
To determine the cheapest cost per bar, compare the cost per bar for each candy bar.
For Candy Bar A:
Cost per bar = Cost / Quantity
For the given values:
- Candy Bar A:
1. $1.25 per bar
2. $1.25 per bar
3. $1.25 per bar
4. $1.25 per bar
5. $1.25 per bar
Therefore, Candy Bar A costs $1.25 per bar.
For Candy Bar B:
Since it is a proportional relationship with y=x, the cost per bar for Candy Bar B would be equal to the quantity.
Therefore, Candy Bar B costs $1 per bar.
Comparing the costs, Candy Bar B (2) is the cheapest cost per bar.
Graphing Linear Equations Unit Test
11 of 1511 of 15 Items
Question
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 1 comma 3 right parenthesis.
Use the graph to derive the equation of the line in slope-intercept form.
To find the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept.
1. Slope (m):
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
Using the points (0, -2) and (1, 3):
m = (3 - (-2)) / (1 - 0)
m = 5 / 1
m = 5
2. Y-intercept (b):
The y-intercept is the point where the line crosses the y-axis. From the given points, we can see that the y-intercept is (0, -2).
3. Write the equation in slope-intercept form:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Substitute the slope m = 5 and y-intercept b = -2 into the equation:
y = 5x - 2
Therefore, the equation of the line in slope-intercept form is y = 5x - 2.
Graphing Linear Equations Unit Test
12 of 1512 of 15 Items
Question
Graph the linear equation y=2x−3.(1 point)
Responses
A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.
The coordinates of the plotted points are as follows: left parenthesis 0 comma 1 right parenthesis, and left parenthesis 1 comma 4 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma 1 right parenthesis, and left parenthesis 1 comma 4 right parenthesis.
An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 1 right parenthesis and left parenthesis 1 comma negative 3 right parenthesis.
Image with alt text: An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 1 right parenthesis and left parenthesis 1 comma negative 3 right parenthesis.
An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 3 right parenthesis and left parenthesis 1 comma 5 right parenthesis.
Image with alt text: An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 3 right parenthesis and left parenthesis 1 comma 5 right parenthesis.
A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.
The coordinates of the plotted points are as follows: left parenthesis 1 comma negative 1 right parenthesis, and left parenthesis 0 comma negative 3 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 1 comma negative 1 right parenthesis, and left parenthesis 0 comma negative 3 right parenthesis.
A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points (0, 1) and (1, 4).
This response incorrectly represents the line for the linear equation y=2x−3. The correct response should be that the line passes through the plotted points (0, -3) and (1, -1).
Write y−6x=5 in slope-intercept form(1 point)
y=
To write the equation y - 6x = 5 in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, we need to solve for y.
Adding 6x to both sides of the equation:
y - 6x + 6x = 5 + 6x
y = 6x + 5
Therefore, the equation y - 6x = 5 in slope-intercept form is y = 6x + 5.