Graph the equation x−y=6

Question

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

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.
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 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.

Answer 1

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

Starting with: \[ x - y = 6 \] we can isolate \( y \): \[ -y = -x + 6 \] Multiplying everything by -1 gives us: \[ y = x - 6 \]

Now, we can identify the slope \( m \) and the y-intercept \( b \):

• The slope \( m = 1 \).
• The y-intercept \( b = -6 \).

This means the line crosses the y-axis at the point \( (0, -6) \).

To find another point on the line, we can use the slope. Since the slope is 1, for each increase of 1 in \( x \), \( y \) also increases by 1.

Starting at the y-intercept \( (0, -6) \):

• If \( x = 1 \), then: \[ y = 1 - 6 = -5 \] So another point is \( (1, -5) \).

With two points, \( (0, -6) \) and \( (1, -5) \), you can plot the line on a graph.

Among the given responses, the illustration that shows the points \( (0, -6) \) and \( (1, -5) \) corresponds to the equation \( y = x - 6 \). Thus, the correct answer is the first illustration you described, which shows a line passing through the points \( (0, -6) \) and \( (1, -5) \).