Graph the equation 2x−y=4

Question

using the form y=mx+b
.(1 point)
Responses

a.
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.

b.
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.

c.
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.

d.
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.

Answer 1

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

Starting with the original equation:

\[2x - y = 4\]

We can isolate \(y\) by adding \(y\) to both sides and subtracting 4:

\[y = 2x - 4\]

Now we can see that the slope \(m\) is 2 and the y-intercept \(b\) is -4. This tells us that the line will cross the y-axis at (0, -4).

Next, we can find another point by selecting a value for \(x\). For example, if we let \(x = 1\):

\[ y = 2(1) - 4 = 2 - 4 = -2 \]

So another point on the line is (1, -2).

To summarize, we have two points to plot: (0, -4) and (1, -2). The line will rise as it proceeds to the right because the slope is positive.

Now let's examine the responses:

• Option a: (0, -4) and (1, 2) - Incorrect because the second point is wrong.
• Option b: (0, 1) and (-2, -2) - Incorrect because both points do not satisfy our line.
• Option c: (0, -4) and (1, -2) - Correct match to our line.
• Option d: (0, -3) and (1, -1) - Incorrect because the points do not match.

Thus, the correct response that represents the graph of the equation \(2x - y = 4\) is:

c. 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 (0, -4) and (1, -2).