Graph the equation 2x−y=4

Question

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

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 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 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 slope-intercept form \(y = mx + b\), we need to rearrange the equation to solve for \(y\).

Starting with the original equation: \[ 2x - y = 4 \]

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

Now, multiply the entire equation by \(-1\) to solve for \(y\): \[ y = 2x - 4 \]

This is now in the form \(y = mx + b\), where:

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

Steps to graph the line:

1. Plot the y-intercept \((0, -4)\).
2. Use the slope to find another point. The slope \(2\) means that for every 1 unit you move to the right (positive direction on the x-axis), you move 2 units up (positive direction on the y-axis). From the point \((0, -4)\), moving 1 unit right to \(x=1\) gives: \[ y = 2(1) - 4 = 2 - 4 = -2 \] So another point is \((1, -2)\).
3. Draw the line through the points \((0, -4)\) and \((1, -2)\) extending in both directions with arrows.

Checking the responses:

The first two responses show lines that do not match the equation correctly. The correct response would be the third illustration since it indicates a solid upward line starting from the y-intercept at \((0, -4)\) and showing another point that follows the slope.

Therefore, the correct graph represents the equation \(y = 2x - 4\):

• The line passes through \((0, -4)\) and follows the slope correctly.

It looks like the third response matches the graph of the equation.