Graph the equation x−y=6

Question

𝑥
−
𝑦
=
6
using the form y=mx+b
𝑦
=
𝑚
𝑥
+
𝑏
.(1 point)
Responses

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.

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.

Answer 1

To graph the equation \( x - y = 6 \) in the form \( y = mx + b \):

1. Start by rearranging the equation to solve for \( y \): \[ x - y = 6 \quad \Rightarrow \quad -y = -x + 6 \quad \Rightarrow \quad y = x - 6 \]

2. Now, we have the equation in slope-intercept form \( y = mx + b \), where:

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

3. To graph the line, start at the y-intercept (0, -6), and from there, use the slope:

   • The slope \( m = 1 \) means for every 1 unit you move to the right on the x-axis, you also move up 1 unit on the y-axis.
   • From (0, -6), moving to the right 1 unit to (1, -5) is one point on the line. Moving another unit to (2, -4) provides another point.

4. You can also move in the opposite direction, starting from the y-intercept at (0, -6), moving left 1 unit down to (-1, -7).

5. After plotting the points (0, -6), (1, -5), (2, -4), and (-1, -7), draw a straight line through these points.

The correct plotting should resemble a line that crosses the y-axis at (0, -6) and is seen rising towards the right as it moves in the direction where both x and y increase.

Given the two responses in your question, neither appears to correctly represent the line for the equation \( x - y = 6 \) or \( y = x - 6 \).

Make sure when graphing this equation, your line passes through the point (0, -6) and maintains a slope of 1.