Graph the linear equation y=−3x+2

Question

.(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.

Answer 1

To graph the linear equation \( y = -3x + 2 \):

First, identify the y-intercept and slope from the equation:

• The y-intercept is \( 2 \) (when \( x = 0 \), \( y = 2 \)).
• The slope is \( -3 \), which means for every increase of \( 1 \) in \( x \), \( y \) decreases by \( 3 \).

Now, let's plot the y-intercept:

• Point: \( (0, 2) \)

Next, use the slope to find another point:

• Starting from \( (0, 2) \), if we go to \( x = 1 \), then \( y = -3(1) + 2 = -1 \).
• Point: \( (1, -1) \)

Now you can plot these two points \( (0, 2) \) and \( (1, -1) \) on the graph.

The line will extend through these points with an overall downward slope.

Therefore, the correct graph should show:

• A downward-sloping line passing through the points \( (0, 2) \) and \( (1, -1) \).

It seems from the descriptions provided, none of the images match the equation \( y = -3x + 2 \). The points mentioned in the other illustrations (such as \( (0, 3) \) and \( (1, 5) \)) don't arise from this equation, nor do the slopes reflect a line with a slope of \(-3\).

So to summarize: The correct points for the graph of \( y = -3x + 2 \) are \( (0, 2) \) and \( (1, -1) \), with the line extending downward through these points.