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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

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 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 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 .
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1 answer

To determine if the graph represents the equation \(3x - y = 10\), let's first rearrange it to the slope-intercept form \(y = mx + b\):

  1. Start with the original equation: \[ 3x - y = 10 \]

  2. Rearranging gives: \[ -y = -3x + 10 \] \[ y = 3x - 10 \]

From this, we can identify that the slope \(m\) is 3 and the y-intercept \(b\) is -10.

Now, let's evaluate the given options based on the y-intercept:

  • The y-intercept (0, −10) indicates that the line crosses the y-axis at -10.
  • The slope of 3 means that for every unit you move right along the x-axis, you move up 3 units along the y-axis.

Given the statement that the line passes through (0, -10) and (1, -7):

  • It confirms that at x=0, y=-10 (which matches our y-intercept).
  • For x=1, substituting into the equation gives: \[ y = 3(1) - 10 = 3 - 10 = -7 \]

This point also aligns with the value on the graph where it passes through (1, -7).

Now we can conclude:

  • The slope is 3.
  • The y-intercept is (0, -10).

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