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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 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 .

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).

1 answer

To determine if the graph represents the equation \(3x - y = 10\), let's convert the equation into slope-intercept form \(y = mx + b\).

Starting with the equation: \[ 3x - y = 10 \]

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

From this, we can see that the slope \(m\) is \(3\) and the y-intercept \(b\) is \(-10\). The y-intercept (0, -10) indicates that when \(x = 0\), \(y = -10\).

Looking at the provided information, the line passes through the points (0, -10) and (1, -7):

  • The point (0, -10) confirms the y-intercept.
  • To calculate the slope using these two points: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-7 - (-10)}{1 - 0} = \frac{3}{1} = 3 \]

Both the slope and y-intercept match those from the equation \(y = 3x - 10\).

Therefore, the correct response is:

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