Graph the equation 2x−y=4

Question

using the form y=mx+b
.(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 negative 2 comma negative 2 right parenthesis and left parenthesis 0 comma 1 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 negative 2 comma negative 2 right parenthesis and left parenthesis 0 comma 1 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 negative 4 right parenthesis and left parenthesis 1 comma 2 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 negative 4 right parenthesis and left parenthesis 1 comma 2 right parenthesis.

An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. An upward slanting line is graphed on the coordinate plane. The upward slanting line passes through closed points plotted at left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma negative 2 right parenthesis.
Image with alt text: An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. An upward slanting line is graphed on the coordinate plane. The upward slanting line passes through closed points plotted at left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma negative 2 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.
Remaining Attempts : 3
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Answer 1

To graph the equation \( 2x - y = 4 \) using the format \( y = mx + b \), we first need to rearrange the equation into slope-intercept form, where \( y \) is isolated on one side.

1. Start with the original equation: \[ 2x - y = 4 \]

2. Subtract \( 2x \) from both sides: \[ -y = -2x + 4 \]

3. Multiply by -1 to get \( y \) by itself: \[ y = 2x - 4 \]

Now, in the equation \( y = 2x - 4 \), the slope \( m \) is \( 2 \) and the y-intercept \( b \) is \( -4 \).

To graph this equation:

• Start at the y-intercept \( (0, -4) \) on the y-axis.
• From this point, use the slope of \( 2 \) (which means rise over run of \( 2/1 \)).
  • From \( (0, -4) \), go up \( 2 \) units and to the right \( 1 \) unit to reach another point on the line: \( (1, -2) \).

You can also find another point by going in the opposite direction. For instance:

• From \( (0, -4) \), you can go down \( 2 \) units (to \( -6 \)) and to the left \( 1 \) unit (to \( -1 \)), which gives you the point \( (-1, -6) \).

The line will pass through:

• \( (0, -4) \)
• \( (1, -2) \)
• \( (-1, -6) \)

Now that we have the points and the slope, we can draw the line extending in both directions through the points.

Among the provided image responses, the correct graph for the equation \( 2x - y = 4 \) (or \( y = 2x - 4 \)) is one that passes through the points \( (0, -4) \) and \( (1, -2) \) which specifically aligns with the linear equation we derived.

Choose the response that corresponds to this description.