Graph the equation x−y=6 using the form y=mx+b.(1 point) Responses Image with alt text: An image is titled Slope-Intercept Form of an Equation. An equation reads y equals m x plus b, where y and x are labeled as the variables of the equation, m is the slope, and b is the y-intercept. The point is left parenthesis 0 comma b 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. 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. 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. Skip to navigation

Question

Graph the equation x−y=6 using the form y=mx+b.(1 point) Responses Image with alt text: An image is titled Slope-Intercept Form of an Equation. An equation reads y equals m x plus b, where y and x are labeled as the variables of the equation, m is the slope, and b is the y-intercept. The point is left parenthesis 0 comma b 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. 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. 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. Skip to navigation

Answer 1

To graph the equation x−y=6 using the form y=mx+b, we need to solve for y.

x−y=6

Subtract x from both sides:

−y=−x+6

Divide both sides by −1:

y=x−6

Now we have the equation in slope-intercept form, where m (the slope) is 1 and b (the y-intercept) is −6.

To graph this equation, we can start at the y-intercept of −6 on the y-axis (0, -6) and then use the slope of 1 to find another point. From (0, -6), we can move up 1 unit and right 1 unit to get to the point (1, -5). We can then draw a line through these two points to represent the equation x−y=6.

The final graph should look like the third image described in the question.