Graph the equation 2x−y=4 using the form y=mx+b.(1 point)

Question

Responses

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.

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.

Answer 1

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

Starting with the original equation:

\[ 2x - y = 4 \]

We can isolate \(y\) by subtracting \(2x\) from both sides:

\[ -y = -2x + 4 \]

Then we multiply both sides by \(-1\) to solve for \(y\):

\[ y = 2x - 4 \]

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

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

To graph this line:

1. Start at the y-intercept (0, -4) on the graph.
2. From that point, use the slope of 2 (which means rise/run = 2/1) to find another point. From (0, -4), go up 2 units and over 1 unit to the right to reach (1, -2).
3. Draw a straight line through these points, extending it in both directions.

Among the given options, the illustration showing an upward slanting line that passes through closed points plotted at (0, -4) and (1, -2) is the correct representation of the equation.