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 downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 1 right parenthesis and left parenthesis 1 comma negative 4 right parenthesis.
Write the equation of the line in slope-intercept form.
(1 point)
Responses
y=−5x+1
y equals negative 5 x plus 1
y=5x+1
y equals 5 x plus 1
y=−5x−1
y equals negative 5 x minus 1
−5x−y=−1
negative 5 x minus y equals negative 1
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To write the equation of the line in slope-intercept form, we need to find the slope and y-intercept.
The slope of a line can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Given the points (0,1) and (1,-4), we can substitute the coordinates into the formula:
m = (-4 - 1) / (1 - 0) = -5 / 1 = -5
The y-intercept can be found by substituting the coordinates of one of the points into the slope-intercept form formula: y = mx + b, where m is the slope and b is the y-intercept.
Using the point (0,1):
1 = -5(0) + b
1 = b
Therefore, the y-intercept, b, is 1.
Now we can write the equation in slope-intercept form:
y = mx + b
So, y = -5x + 1
The correct answer is:
y = -5x + 1
Graphing Equations Quick Check
3 of 53 of 5 Items
Question
Graph the linear equation y=−3x+2.(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 negative 2 comma 2 right parenthesis, and left parenthesis 0 comma 1 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 negative 2 comma 2 right parenthesis, and left parenthesis 0 comma 1 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. he line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 1 comma negative 5 right parenthesis. A dotted vertical line labeled 3 from left parenthesis 1 comma negative 5 right parenthesis and a dotted horizontal line labeled 1 from left parenthesis 0 comma negative 2 right parenthesis intersect at left parenthesis 1 comma negative 2 right parenthesis, forming a right triangle with the slope.
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. he line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 1 comma negative 5 right parenthesis. A dotted vertical line labeled 3 from left parenthesis 1 comma negative 5 right parenthesis and a dotted horizontal line labeled 1 from left parenthesis 0 comma negative 2 right parenthesis intersect at left parenthesis 1 comma negative 2 right parenthesis, forming a right triangle with the slope.
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 2 right parenthesis, and left parenthesis 1 comma negative 1 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 2 right parenthesis, and left parenthesis 1 comma negative 1 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.
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To graph the linear equation y = -3x + 2, we need to plot two points on the coordinate plane and draw a line through them.
The given points are (-2, 2) and (0, 1).
Plotting these points on the coordinate plane, we get:
(-2, 2) is plotted on the coordinate (-2,2).
(0, 1) is plotted on the coordinate (0,1).
Now, we can draw a line through these two points. The line should have arrows at both ends to indicate that it continues indefinitely in both directions.
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 the plotted points (-2,2) and (0,1).
The correct response is:
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 the plotted points (-2,2) and (0,1).
Use the image to answer the question.
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 3 right parenthesis, and left parenthesis 3 comma 2 right parenthesis.
Is this the correct graph of y=−13x+4?(1 point)
Responses
No, it is not the correct graph because this graph used (0,3) as the y-intercept.
No, it is not the correct graph because this graph used left parenthesis 0 comma 3 right parenthesis as the y -intercept.
Yes, it is the correct graph because this graph has a y-intercept of (0,3).
Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 3 right parenthesis .
Yes, it is the correct graph because this graph has a y-intercept of (0,4).
Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 4 right parenthesis .
No, it is not the correct graph because this graph has a positive slope.
No, it is not the correct graph because this graph has a positive slope.
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To determine if the given graph is the correct graph of the equation y = -13x +4 , we need to compare the graph's features with the features of the equation.
The equation y = -13x + 4 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
From the graph, we can see that the line passes through the points (0,3) and (3,2).
Comparing this with the equation, we can see that the y-intercept is (0,3), which matches the y-intercept in the equation.
Therefore, the correct answer is:
Yes, it is the correct graph because this graph has a y-intercept of (0,3).
To find the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept.
First, let's find the slope (m) using the two given points:
(0, 1) and (1, -4)
The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates:
m = (-4 - 1) / (1 - 0)
m = -5
Now that we have the slope (m), we can use the formula of a straight line (slope-intercept form) y = mx + b, where m is the slope and b is the y-intercept.
Next, let's find the y-intercept (b) using one of the given points. Let's use (0, 1):
1 = -5(0) + b
1 = b
Now that we have the slope (m = -5) and the y-intercept (b = 1), we can write the equation of the line in slope-intercept form:
y = -5x + 1
Therefore, the correct answer is:
y = -5x + 1
To find the equation of a line in slope-intercept form, which is y = mx + b, we need to determine the slope (m) and the y-intercept (b).
From the given information, we can identify two points on the line: (0, 1) and (1, -4).
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (0, 1) and (1, -4):
m = (-4 - 1) / (1 - 0)
m = -5/1
m = -5
Now that we have the slope (m = -5), we can substitute it into the equation:
y = mx + b
Using the point (0, 1) and the slope (-5):
1 = -5(0) + b
1 = b
So, the y-intercept (b) is 1.
Putting the slope (m = -5) and the y-intercept (b = 1) into the equation, we get:
y = -5x + 1
Therefore, the equation of the line in slope-intercept form is:
y = -5x + 1
The correct answer is:
y = -5x + 1