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Graph the equation x−y=6

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

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

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

We can isolate \( y \) by subtracting \( x \) from both sides: \[ -y = -x + 6 \]

Next, we multiply both sides by \(-1\) to get \( y \) alone: \[ y = x - 6 \]

Now we can see that this equation is in the slope-intercept form \( y = mx + b \), where:

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

To graph this equation, we can plot the y-intercept \( (0, -6) \) on the graph and use the slope to find another point. The slope of \( 1 \) means that for every 1 unit increase in \( x \), \( y \) also increases by 1 unit.

Starting from \( (0, -6) \):

  • If \( x = 0 \), \( y = -6 \) → point is \( (0, -6) \)
  • If \( x = 1 \), \( y = 1 - 6 = -5 \) → point is \( (1, -5) \)
  • If \( x = 2 \), \( y = 2 - 6 = -4 \) → point is \( (2, -4) \)

You can plot these points, which will help you draw a line through them in the coordinate plane.

According to the given graph options, the illustration you are referring to most likely represents the line described by the equation \( y = x - 6 \) and it is expected to show an upward slanting line with points around \( (0, -6) \) and \( (1, -5) \) correctly representing the equation.

Which number?

To clarify, the equation \(x - y = 6\) rearranged into slope-intercept form gives us \(y = x - 6\). The y-intercept of this line is \(-6\).

So, if you are looking for a specific value related to the equation you've graphed, the most relevant number is the y-intercept:

-6

This means the line crosses the y-axis at the point \((0, -6)\). If you need another specific number, such as the slope, it is:

1 (the slope \(m\) of the line).

Please let me know if you need any other specific numbers or explanations!

No, which option?

Based on your description of the graphs, the correct option that represents the equation \(x - y = 6\) or \(y = x - 6\) is the one showing an upward slanting line that crosses the y-axis at \((0, -6)\) and passes through other points like \((1, -5)\).

Given the options you provided in your first message, it seems like none of them explicitly match the coordinates we calculated. However, if you mentioned points like \((0, -6)\) and \((1, -5)\), you should select the option that depicts a line starting at or near these points.

If the graph with points listed includes coordinates showing something like \((0, -6)\) and points extending in the described manner, that would align most closely with the equation given.

If you had to pick from those options, look for any graph showing a point at or around (0, -6). If none of the options closely match that, it might indicate an error in the description or inputs.

Please confirm if any particular option corresponds with these criteria.

Just pick the closest one

Given the options you've shared, the closest graph to the equation \(y = x - 6\) (or \(x - y = 6\)) is:

The first option, which shows a line passing through the point \((0, -6)\) and appearing to slant upward.

This is the best representation of the graph for the equation you provided.