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Graphing Equations Quick Check
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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 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.

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.
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1 answer

To graph the linear equation \( y = -3x + 2 \), let's analyze the equation:

  1. Identify the y-intercept: The y-intercept is the value of \( y \) when \( x = 0 \). From the equation, when \( x = 0 \): \[ y = -3(0) + 2 = 2 \] So the point \( (0, 2) \) is on the graph.

  2. Calculate another point using the slope: The slope of the line is \(-3\), which means for every increase of \(1\) in \(x\), \(y\) decreases by \(3\). Starting at the y-intercept \( (0, 2) \):

    • If \( x = 1 \): \[ y = -3(1) + 2 = -1 \] So the point \( (1, -1) \) is also on the graph.

  3. Plot the points and draw the line:

    • Plot the points \( (0, 2) \) and \( (1, -1) \) on the coordinate plane. Draw a line through these points that extends in both directions.

Given the context of the responses to your question, the correct graph representation of the equation \( y = -3x + 2 \) would be the one that includes the points \( (0, 2) \) and \( (1, -1) \), along with a correctly drawn line having a negative slope.

Conclusion:

The correct representation corresponds to the description of a solid downward line passing through the points (0, 2) and (1, -1). Based on your provided options, it seems that none of the provided graphs exactly correspond to the equation \( y = -3x + 2 \). However, the first description with the points (0, 2) and (1, -1) is the only one consistent with the equation \( y = -3x + 2 \).