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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.

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 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.

1 answer

To graph the linear equation \( y = 2x - 3 \), we can follow these steps:

  1. Identify the slope and y-intercept: The equation \( y = 2x - 3 \) is already in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Here, the slope \( m \) is 2, and the y-intercept \( b \) is -3.

  2. Plot the y-intercept: The y-intercept is the point at which the line crosses the y-axis. For this equation, it is the point (0, -3).

  3. Use the slope to find another point: The slope of 2 means that for every 1 unit you move to the right along the x-axis, you move up 2 units. From (0, -3), move 1 unit to the right to (1, -3 + 2) = (1, -1).

  4. Plot the second point: Plot the second point (1, -1) on the graph.

  5. Draw the line: Connect the two points with a straight line and extend the line in both directions with arrows.

So, the graph of the equation \( y = 2x - 3 \) should show a line passing through the points (0, -3) and (1, -1), sloping upward.

Now let's identify which response matches this description:

  • The correct points should be (0, -3) and (1, -1).

None of the provided options match the correct points for the graph of \( y = 2x - 3 \). The correct graph would show a line going through the points (0, -3) and (1, -1), and it would have a positive slope (going upwards from left to right).