Graph the equation x−y=6

Question

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

An illustration shows a coordinate plane with the x-axis ranging from negative 9 to 9 in one unit increments, and the y-axis ranging from negative 11 to 11 in one unit increments. A solid line passes through two plotted points and extends beyond. A solid line with arrows at both ends passes through points with coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 right parenthesis.
Image with alt text: An illustration shows a coordinate plane with the x-axis ranging from negative 9 to 9 in one unit increments, and the y-axis ranging from negative 11 to 11 in one unit increments. A solid line passes through two plotted points and extends beyond. A solid line with arrows at both ends passes through points with coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 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 0 comma 3 right parenthesis, and left parenthesis 3 comma 2 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 0 comma 3 right parenthesis, and left parenthesis 3 comma 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 0 comma negative 4 right parenthesis, and left parenthesis 1 comma negative 10 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 0 comma negative 4 right parenthesis, and left parenthesis 1 comma negative 10 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 6 right parenthesis and left parenthesis 1 comma negative 5 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 6 right parenthesis and left parenthesis 1 comma negative 5 right parenthesis.
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Answer 1

To graph the equation \(x - y = 6\) using the form \(y = mx + b\), we first need to rearrange the equation into slope-intercept form (where \(y\) is isolated).

Starting with the original equation: \[ x - y = 6 \]

We can solve for \(y\): \[ -y = -x + 6 \] \[ y = x - 6 \]

Here, the slope (\(m\)) is \(1\), and the y-intercept (\(b\)) is \(-6\).

Now, we can plot the line:

1. Y-intercept: Start by plotting the y-intercept (0, -6).
2. Slope: From there, use the slope to find another point. Since the slope is \(1\), it means that for every 1 unit increase in \(x\), \(y\) increases by 1 unit. So from (0, -6), moving to the right to \(x = 1\), we go up to \(y = -5\), giving us the point (1, -5).
3. Draw the line: Draw a line through these points, extending it in both directions.

Based on these calculations, the graph should represent a line that passes through points like (0, -6) and (1, -5). This will not match any of the previous options you've listed, but it describes how to graph the equation accurately. If you had to select from the options given, none of them correctly represents the line for the equation \(x - y = 6\).