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Graph the equation x−y=6 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.

1 answer

To graph the equation \( x - y = 6 \) in the form \( y = mx + b \), we first need to rearrange the equation.

Starting with: \[ x - y = 6 \]

We isolate \( y \) by subtracting \( x \) from both sides: \[ -y = -x + 6 \]

Now, multiplying through by -1 gives us: \[ y = x - 6 \]

This equation is now in slope-intercept form (where \( m = 1 \) and \( b = -6 \)).

To graph this equation, we can identify two key points:

  1. When \( x = 0 \): \[ y = 0 - 6 = -6 \] So, one point is \( (0, -6) \).

  2. When \( x = 6 \): \[ y = 6 - 6 = 0 \] So, another point is \( (6, 0) \).

Plot these two points on the graph:

  • Point \( (0, -6) \) is on the y-axis.
  • Point \( (6, 0) \) is on the x-axis.

Now, draw a straight line through these two points, which will extend infinitely in both directions. This line represents the equation \( x - y = 6 \) or \( y = x - 6 \).

From the provided responses, the illustration showing a line that passes through points \( (0, -6) \) would be the correct graph for the equation \( x - y = 6 \). However, none of the descriptions perfectly match the points derived from the equation, so if you create this graph, ensure to mark the mentioned points accurately.