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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 10 right parenthesis and left parenthesis 1 comma negative 7 right parenthesis.

Is this the correct graph of 3x−y=10?

(1 point)
Responses

Yes, it is the correct graph because the slope is −3 and the y-intercept is (0, −10).
Yes, it is the correct graph because the slope is negative 3 and the y -intercept is left parenthesis 0 comma negative 10 right parenthesis .

No, it is not the correct graph because the slope is −3 and the y-intercept is (0, −10).
No, it is not the correct graph because the slope is negative 3 and the y -intercept is left parenthesis 0 comma negative 10 right parenthesis .

Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, −10).
Yes, it is the correct graph because the slope is 3 and the y -intercept is left parenthesis 0 comma negative 10 right parenthesis .

No, it is not the correct graph because the slope is 3 and the y-intercept is (0, −10).

1 answer

To determine if the given graph correctly represents the equation \(3x - y = 10\), let's first rewrite it in slope-intercept form \(y = mx + b\).

Starting with \(3x - y = 10\):

  1. Subtract \(3x\) from both sides: \[-y = -3x + 10\]

  2. Multiply through by -1 to change the signs: \[y = 3x - 10\]

In this equation, we can see that the slope \(m\) is \(3\) and the y-intercept \(b\) is \(-10\), which means the y-intercept point is \((0, -10)\).

Now, analyzing the original question regarding the graph's characteristics:

  1. The slope of the line should be \(3\) (upward slanting).
  2. The y-intercept of the line should be at \((0, -10)\).

Since the analysis shows that the slope is \(3\) and the y-intercept is indeed at \((0, -10)\), the correct response to whether this is the correct graph of \(3x - y = 10\) is:

Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, −10).