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

Question

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.

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.
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Answer 1

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

Starting with the original equation: \[ x - y = 6 \]

We can solve for \( y \): \[ -y = -x + 6 \] \[ y = x - 6 \]

Now we can identify the slope \( m \) and the y-intercept \( b \) from the equation \( y = mx + b \):

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

Using this information, we can plot the line on a graph:

1. Start at the y-intercept (0, -6).
2. From this point, use the slope to find another point. The slope of \( 1 \) means that for every 1 unit you move right (positive x-direction), you move up 1 unit (positive y-direction).

Plotting a couple of points based on the equation:

• Starting at (0, -6), moving right 1 unit gives (1, -5).
• Moving right another unit gives (2, -4).

Now draw a straight line through these points, extending it in both directions.

The correct option based on the choices provided is likely the one that depicts a line with a slope of 1 and passing through the point (0, -6) and (1, -5).

Answer 2

ok so a b c or d

Answer 3

Given the points I've described and the equation \( y = x - 6 \), the correct choice would be the one that has the line passing through (0, -6) and (1, -5).

Assuming the following responses based on the images you described:

1. Response A: Points (0, -6) and (1, -5) - This is the correct choice.
2. Response B: Points (0, 3) and (3, 2) - Incorrect.
3. Response C: Points (0, 0) and (6, 6) - Incorrect.
4. Response D: Points (0, -4) and (1, -10) - Incorrect.

So, Response A is the correct answer.