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Graph the equation x−y=6

using the form y=mx+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 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 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.

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.

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.

1 answer

To graph the equation \(x - y = 6\) using the form \(y = mx + b\), we first convert the equation into slope-intercept form (which is \(y = mx + b\)).

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

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

Multiplying through by -1 gives us: \[ y = x - 6 \]

Now, in this equation \(y = x - 6\), the slope \(m\) is \(1\) and the y-intercept \(b\) is \(-6\).

To graph this equation:

  • Start at the y-intercept \((0, -6)\).
  • From there, use the slope: for every 1 unit you move to the right (positive direction on the x-axis), you move up 1 unit (positive direction on the y-axis).

You can also find another point by plugging in another value for \(x\):

  • If \(x = 3\): \[ y = 3 - 6 = -3 \] So another point is \((3, -3)\).

Plotting the points \((0, -6)\) and \((3, -3)\) and drawing a line through them gives the graph of the equation.

Given your descriptions, the correct image would be the one where a line drawn through points includes the coordinates (0, -6) as this corresponds correctly with our derived equation \(y = x - 6\).

The specific plotting of other points from your options does not seem to match the equation \(x - y = 6\) or \(y = x - 6\) correctly, so please refer to the graph that clearly shows that relationship. If you can provide those images or correct specific coordinates as needed, I can further assist!