Graphing Linear Equations Unit Test

Question

Graphing Linear Equations Unit Test
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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 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.

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 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.

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.

GPT-4o mini · Answer

To graph the linear equation $ y = 2x - 3 $, we should first identify a couple of points that lie on this line. We can do this by choosing values for $ x $ and calculating the corresponding $ y $ values. 1. When $ x = 0 $: $$ y = 2(0) - 3 = -3 $$ So one point is $ (0, -3) $. 2. When $ x = 1 $: $$ y = 2(1) - 3 = -1 $$ So another point is $ (1, -1) $. 3. When $ x = 2 $: $$ y = 2(2) - 3 = 1 $$ So a third point is $ (2, 1) $. Now you can plot these points: $ (0, -3) $, $ (1, -1) $, and $ (2, 1) $. The slope of the line is 2, indicating that for every 1 unit increase in $ x $, $ y $ increases by 2 units. Looking at the response options provided: - The first option shows a line that is downward sloping and has points $ (0, -1) $ and $ (1, -3) $ which does not match our equation. - The second option shows an upward sloping line with points $ (0, 3) $ and $ (1, 5) $, which also does not match. - The third option shows points $ (1, -1) $ and $ (0, -3) $, but it shows the line going downward. - The fourth option shows points $ (0, 1) $ and $ (1, 4) $, which does not match either. The correct graph of the line $ y = 2x - 3 $ should show an upward slope, passing through $ (0, -3) $, $ (1, -1) $, and continuing to rise as $ x $ increases. None of the options given seem to represent the correct line. If there was a graph showing an upward slope passing through the points (for example, $ (0, -3) $ and $ (2, 1) $), that would be the correct choice. Since none of the options fit, it's possible there's either an error in the available graphs or a misunderstanding in which points are being displayed.