Graph the linear equation y=2x−3

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 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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Answer 1

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.