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.

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 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.
Remaining Attempts : 3
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Answer 1

To graph the equation \(2x - y = 4\) in the slope-intercept form \(y = mx + b\), we first need to rearrange it into that format.

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

2. Isolate \(y\) by moving \(2x\) to the other side: \[ -y = -2x + 4 \]

3. Multiply through by \(-1\) to solve for \(y\): \[ y = 2x - 4 \]

Now we can identify the slope \(m\) and y-intercept \(b\):

• The slope \(m = 2\)
• The y-intercept \(b = -4\)

This means the line crosses the y-axis at \( (0, -4) \).

Next, we can find another point by plugging in a value for \(x\):

• If \(x = 1\): \[ y = 2(1) - 4 = 2 - 4 = -2 \] So another point is \( (1, -2) \).

Now we can plot these points:

• The first point is \( (0, -4) \).
• The second point is \( (1, -2) \).

Draw a line through these points, and it will extend infinitely in both directions. The line will slope upward from left to right due to the positive slope.

In the context of the options provided, the correct representation of the graph will likely be the one showing the line passing through points that match the coordinates from our calculation (e.g., \( (0, -4) \) and \( (1, -2) \)).

Therefore, based on the final equation \(y = 2x - 4\), you should look for an illustration that matches the characteristics discussed:

• The line crosses the y-axis at \( (0, -4) \)
• It should pass through the point \( (1, -2) \) as well.

Please check the graph options to find the one that accurately represents this.