Graph the linear equation y=−3x+2

Question

Graph the linear equation y=−3x+2
.(1 point)
Responses

A coordinate1 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 2 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 coordinate3 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 plane4 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.
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GPT-4o mini · Answer

To graph the linear equation $ y = -3x + 2 $, you need to identify two points that lie on the line and then connect those points with a line. 1. **Finding Points**: - Start by plugging in values for $ x $ to find corresponding $ y $ values. - For $ x = 0 $: $$ y = -3(0) + 2 = 2 \quad \Rightarrow \quad (0, 2) $$ - For $ x = 1 $: $$ y = -3(1) + 2 = -1 \quad \Rightarrow \quad (1, -1) $$ - For $ x = -1 $: $$ y = -3(-1) + 2 = 5 \quad \Rightarrow \quad (-1, 5) $$ - For $ x = -2 $: $$ y = -3(-2) + 2 = 8 \quad \Rightarrow \quad (-2, 8) $$ 2. **Plotting Points**: - Plot the points $ (0, 2) $, $ (1, -1) $, $ (-1, 5) $, and $ (-2, 8) $ on the graph. 3. **Drawing the Line**: - Connect these points with a straight line that extends in both directions, adding arrows at the ends of the line to show that it continues indefinitely. Now, from the responses provided, you would look for the option that properly illustrates the line passing through at least a couple of these points. Among the options, the one that mentions points $ (0, 2) $ and $ (1, -1) $ is the correct match. **Final Answer**: The graph described with points $ (0, 2) $ and $ (1, -1) $ accurately represents the line $ y = -3x + 2 $.