Graph the equation x−y=6

Question

using the form y=mx+b
.(1 point)
Responses

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.

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.

Answer 1

To graph the equation \( x - y = 6 \) in the form \( y = mx + b \), we need to rewrite it as follows:

1. Start with the equation: \[ x - y = 6 \]

2. Solve for \( y \): \[ -y = -x + 6 \] \[ y = x - 6 \]

Now that we have the equation in slope-intercept form \( y = mx + b \), where \( m = 1 \) (the slope) and \( b = -6 \) (the y-intercept), we can identify the y-intercept and a point to plot.

• The y-intercept is \( (0, -6) \).
• To find another point, choose \( x = 6 \): \[ y = 6 - 6 = 0 \implies (6, 0) \]

Now we can plot the points \( (0, -6) \) and \( (6, 0) \) on a coordinate plane and draw a line through them.

From the provided options, the response that best fits is a depiction that shows a line with a positive slope passing through points like \( (0, -6) \) and \( (6, 0) \).

Given that none of the descriptions provided explicitly match the points derived from the equation, it seems that the equation \( x - y = 6 \) leads us to select the option that shows a line with the aforementioned characteristics—specifically the one that captures the correct slope and y-intercept orientation.

If the option depicting the line described is included, select that one. The correct graph would show a line passing through \( (0, -6) \) with a slope of 1, indicating the relationship defined by this linear equation.

Answer 2

is the answer A,B,C, OR D

Answer 3

To determine the correct choice based on the equation \( x - y = 6 \) rewritten as \( y = x - 6 \):

1. Slope (m): The slope is 1, which means for every unit increase in \( x \), \( y \) increases by 1.
2. Y-intercept (b): The y-intercept is -6, meaning the line crosses the y-axis at (0, -6).

Given these characteristics, let's examine the options more closely:

• Choice A: It mentions points \( (0, 0) \) and \( (6, 6) \). This does not represent the line described by \( y = x - 6 \).

• Choice B: It mentions points \( (0, -4) \) and \( (1, -10) \), which also does not fit our line.

• Choice C: This option shows points \( (0, -6) \) and \( (1, -5) \). This line has a positive slope and matches the line we derived, so this could be correct, but the second point is not accurate as per our equation.

• Choice D: It mentions points \( (0, 3) \) and \( (3, 2) \), which does not fit the line we derived.

Given this analysis:

None of the options accurately represent \( y = x - 6 \), but Choice C comes the closest with a slope that reflects the correct upward trend, even though the second point is not exact.

If you must choose from the options, then select Choice C, as it shows a line with an upward slope and a y-intercept near -6.