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 4 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.
Using the graph, derive the equation of the line in slope-intercept form.
(1 point)
Responses
y=3x+4
y equals 3 x plus 4
y=3x−4
y equals 3 x minus 4
y=−3x−4
y equals negative 3 x minus 4
3x−y=4
To derive the equation of the line in slope-intercept form, we need to first find the slope of the line. The slope can be determined using the two given points on the line.
The slope (m) is calculated by dividing the change in y-coordinates by the change in x-coordinates between the two points.
In this case, the two points on the line are (0, -4) and (1, -1).
Using the formula for slope: m = (y2 - y1) / (x2 - x1), we can calculate the slope:
m = (-1 - (-4)) / (1 - 0)
m = (-1 + 4) / 1
m = 3/1
m = 3
The slope of the line is 3.
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line.
The point-slope form is y - y1 = m(x - x1), where (x1, y1) is one of the given points.
Let's choose the point (0, -4) to substitute into the equation.
y - (-4) = 3(x - 0)
y + 4 = 3x
To rewrite the equation in slope-intercept form (y = mx + b), we need to isolate y.
Subtract 4 from both sides of the equation:
y = 3x - 4
Therefore, the equation of the line in slope-intercept form is y = 3x - 4.
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
−5x−y=−1
negative 5 x minus y equals negative 1
y=−5x+1
y equals negative 5 x plus 1
y=−5x−1
y equals negative 5 x minus 1
y=5x+1
y equals 5 x plus 1
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To derive the equation of the line in slope-intercept form, we need to first find the slope of the line. The slope can be determined using the two given points on the line.
The slope (m) is calculated by dividing the change in y-coordinates by the change in x-coordinates between the two points.
In this case, the two points on the line are (0, 1) and (1, -4).
Using the formula for slope: m = (y2 - y1) / (x2 - x1), we can calculate the slope:
m = (-4 - 1) / (1 - 0)
m = (-4 - 1) / 1
m = -5/1
m = -5
The slope of the line is -5.
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line.
The point-slope form is y - y1 = m(x - x1), where (x1, y1) is one of the given points.
Let's choose the point (0, 1) to substitute into the equation.
y - 1 = -5(x - 0)
y - 1 = -5x
To rewrite the equation in slope-intercept form (y = mx + b), we need to isolate y.
Add 1 to both sides of the equation:
y = -5x + 1
Therefore, the equation of the line in slope-intercept form is y = -5x + 1.
Graph the linear equation y=−3x+2.(1 point)
Responses
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 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.
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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I'm sorry, I cannot view or process images. However, I can provide you with the steps to graph the linear equation y = -3x + 2.
1. Plot the two given points on the coordinate plane:
- Point 1: (0, 2)
- Point 2: (1, 5)
2. Draw a straight line that passes through both plotted points. Make sure to extend the line with arrows at both ends.
The resulting graph should show a solid line with a downward slope that passes through the points (0, 2) and (1, 5).
Graph the linear equation y=−3x+2.(1 point)
Responses
To graph the linear equation y = -3x + 2, follow these steps:
1. Set up a coordinate plane with the x-axis ranging from -9 to 9 and the y-axis ranging from -11 to 11 in increments of 1.
2. Plot two points on the graph using the coordinates (0, 2) and (1, -1). The first point represents the y-intercept of the equation (when x is 0, y is 2), and the second point represents another point on the line.
3. Draw a straight line that passes through both plotted points. The line should extend in both directions.
The resulting graph will show a downward sloping line that intersects the y-axis at y = 2.
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 (0,4).
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.
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 .
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The correct answer is:
No, it is not the correct graph because this graph has a positive slope.
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