Graph the equation x−y=6

Question

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.

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.

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.
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GPT-4o mini · Answer

To graph the equation $ x - y = 6 $ in the form $ y = mx + b $: 1. Start with the original equation: $$ x - y = 6 $$ 2. Rearrange it to solve for $ y $: $$ -y = -x + 6 $$ $$ y = x - 6 $$ In this form, we can identify: - The slope $ m = 1 $ - The y-intercept $ b = -6 $ ### Plotting the Line 1. **Y-Intercept**: Start by plotting the point where the line crosses the y-axis (when $ x = 0 $): $$ y = 0 - 6 = -6 $$ So, plot the point $ (0, -6) $. 2. **Using the slope**: From the y-intercept, use the slope to find another point. Since the slope is $ 1 $, it means that for every 1 unit you move up, you move 1 unit to the right: - From $ (0, -6) $, move right 1 unit to $ (1, -5) $ (up 1 from $ -6 $). 3. **Additional Points**: You can continue this process: - Move to $ (2, -4) $ - Move to $ (3, -3) $ - Continue to plot more points if needed. 4. **Draw the Line**: Once you have plotted at least two points, draw a straight line through them, extending it in both directions with arrows on either end. ### Conclusion Based on the modifications, the graph of the equation $ x - y = 6 $ will be a straight line with a slope of $ 1 $ intersecting the y-axis at $ -6 $. None of the plotted points in the options you've provided align with this equation. The correct points should reflect the location of the line defined by $ y = x - 6 $ based on the calculations above.