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.

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.

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.
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GPT-4o mini · Answer

To graph the linear equation $ y = 2x - 3 $, let's identify some points on the line by substituting values for $ x $: 1. **When $ x = 0 $**: $$ y = 2(0) - 3 = -3 $$ This gives the point $ (0, -3) $. 2. **When $ x = 1 $**: $$ y = 2(1) - 3 = -1 $$ This gives the point $ (1, -1) $. 3. **When $ x = 2 $**: $$ y = 2(2) - 3 = 1 $$ This gives the point $ (2, 1) $. Now we have three points that lie on the line: $ (0, -3) $, $ (1, -1) $, and $ (2, 1) $. Once plotted on the coordinate plane: - The point $ (0, -3) $ is on the y-axis. - The point $ (1, -1) $ is one unit to the right and one unit up from the origin. - The point $ (2, 1) $ is two units to the right and one unit up from the previous point. A line drawn through these points will be the graphical representation of the equation. The line has a positive slope of 2 (indicating it rises 2 units for every 1 unit it moves to the right) and crosses the y-axis at -3. Given this information, the correct illustration of the graph for $ y = 2x - 3 $ will show a line passing through the points $ (0, -3) $ and $ (1, -1) $, and will extend infinitely with arrows at both ends. The options you provided include incorrect representations of the graph. None of the points or slopes match $ y = 2x - 3 $. The correct graphical representation will not be among the options you've listed.