Graph the linear equation y=2x−3

Question

Graph the linear equation y=2x−3
.(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 1 right parenthesis, and left parenthesis 1 comma 4 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 1 right parenthesis, and left parenthesis 1 comma 4 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. The line passes through the plotted points left parenthesis 0 comma negative 1 right parenthesis and left parenthesis 1 comma negative 3 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 downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 1 right parenthesis and left parenthesis 1 comma negative 3 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 1 comma negative 1 right parenthesis, and left parenthesis 0 comma negative 3 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 1 comma negative 1 right parenthesis, and left parenthesis 0 comma negative 3 right parenthesis.

GPT-4o mini · Answer

To graph the equation $ y = 2x - 3 $, we can identify key points on the line by substituting values for $ x $. 1. **Finding Points**: - When $ x = 0 $: $$ y = 2(0) - 3 = -3 \quad \Rightarrow \quad (0, -3) $$ - When $ x = 1 $: $$ y = 2(1) - 3 = -1 \quad \Rightarrow \quad (1, -1) $$ - When $ x = 2 $: $$ y = 2(2) - 3 = 1 \quad \Rightarrow \quad (2, 1) $$ 2. **Plotting Points**: You would plot the points $ (0, -3) $, $ (1, -1) $, and $ (2, 1) $ on the coordinate plane. 3. **Drawing the Line**: After plotting the points, draw a straight line through them, extending the line with arrows on both ends. Based on the provided choices, the only option that correctly reflects the required points and the correct direction is: - The option with the coordinates $ (0, -3) $ and $ (1, -1) $. The line you need to graph should look like it passes through $ (0, -3) $ and $ (1, -1) $ and is moving upwards, confirming that it follows the equation $ y = 2x - 3 $. Thus, the correct image representation would correspond to a line passing through the points $ (0, -3) $ and $ (1, -1) $.