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 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.

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.
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Answer 1

To graph the linear equation \( y = 2x - 3 \), we'll identify two key points and then draw the line through them.

1. Find the y-intercept (when \( x = 0 \)): \[ y = 2(0) - 3 = -3 \] So, the point is \( (0, -3) \).

2. Choose another value for \( x \) to find a corresponding \( y \) value (let's use \( x = 1 \)): \[ y = 2(1) - 3 = 2 - 3 = -1 \] So, the point is \( (1, -1) \).

Now, we can plot these points on a graph:

• The point \( (0, -3) \) indicates where the line crosses the y-axis.
• The point \( (1, -1) \) gives us another point on the line.

3. Draw the line: Connect the two points with a straight line and extend it with arrows on both ends.

Choosing from the provided descriptions, the correct graph should show a line that passes through the points \( (0, -3) \) and \( (1, -1) \), consistent with the equation \( y = 2x - 3 \).

None of the provided responses accurately described the correct graph of the equation \( y = 2x - 3 \), but based on our analysis, it should be a line passing through \( (0, -3) \) and \( (1, -1) \).