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

Question

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 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 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.

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.
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GPT-4o mini · Answer

To graph the linear equation $ y = -3x + 2 $, we can identify some key points by substituting values for $ x $. 1. **Finding Points:** - **When $ x = 0 $:** $$ y = -3(0) + 2 = 2 \quad \Rightarrow \quad (0, 2) $$ - **When $ x = 1 $:** $$ y = -3(1) + 2 = -1 \quad \Rightarrow \quad (1, -1) $$ - **When $ x = -1 $:** $$ y = -3(-1) + 2 = 5 \quad \Rightarrow \quad (-1, 5) $$ - **When $ x = 2 $:** $$ y = -3(2) + 2 = -4 \quad \Rightarrow \quad (2, -4) $$ From these calculations, we have identified the points: - $ (0, 2) $ - $ (1, -1) $ - $ (-1, 5) $ - $ (2, -4) $ 2. **Plotting the Points:** On a coordinate plane, mark the points $ (0, 2) $, $ (1, -1) $, $ (-1, 5) $, and $ (2, -4) $. 3. **Drawing the Line:** Connect these points with a straight line, extending it with arrows on both ends to indicate that it goes on infinitely. 4. **Identifying Characteristics:** The slope of the line is -3, indicating it will descend as it moves from left to right. The y-intercept (the point where the line crosses the y-axis) is at $ (0, 2) $. Based on this analysis, the correct graph representation should show a downward sloping line passing through the points identified, particularly through $ (0, 2) $ and $ (1, -1) $. ### Conclusion: The correct illustration would not match any of the provided options directly. However, the key points to look for are the characteristic downward slope and those specific points derived from your equation. If you have a choice to select graphics, look for one that best matches this description with points like $ (0, 2) $ and has a negative slope.