Graph the equation x−y=6

Question

Graph the equation x−y=6
 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.

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 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.

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.

GPT-4o mini · Answer

To graph the equation $ x - y = 6 $ using the slope-intercept form $ y = mx + b $, we first need to rearrange the equation. 1. Start with the original equation: $$ x - y = 6 $$ 2. Solve for $ y $: $$ -y = -x + 6 $$ $$ y = x - 6 $$ Now, we can see that this is in the form $ y = mx + b $ where $ m = 1 $ (the slope) and $ b = -6 $ (the y-intercept). ### Steps to graph the equation: - **Y-Intercept:** Start by plotting the y-intercept (0, -6) on the coordinate plane. This is where the line crosses the y-axis. - **Slope:** The slope $ m = 1 $ means that for every 1 unit you move to the right on the x-axis, you move 1 unit up on the y-axis. From (0, -6), the next point can be (1, -5). - **Plot another point:** Continuing from (1, -5), we can go to (2, -4). - **Draw the line:** Draw a straight line through the points you plotted (0, -6) and (1, -5) and extend it in both directions. ### Final Graph You would see an upward slanting line starting from (0, -6) and increasing as you plot more points according to the slope. Let me know if you need any additional help or information!