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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 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)
.

1 answer

To determine whether the graph represents the equation \(3x - y = 10\), we need to analyze the slope and y-intercept of the line.

  1. Rearranging the Equation:
    Start with the equation \(3x - y = 10\).
    Rearranging it to slope-intercept form (\(y = mx + b\)): \[ -y = -3x + 10 \quad \text{(add } y \text{ to both sides)}
    y = 3x - 10 \] Here, the slope (\(m\)) is 3, and the y-intercept (\(b\)) is \(-10\), meaning the line crosses the y-axis at point (0, -10).

  2. Checking Points on the Graph:
    The graph mentions points (0, -10) and (1, -7):

    • The point (0, -10) matches the y-intercept from our equation.
    • To check the point (1, -7): Substitute \(x = 1\) in the equation \(y = 3x - 10\): \[ y = 3(1) - 10 = 3 - 10 = -7 \] Thus, the point (1, -7) is also on the line.

  3. Conclusion:
    The slope from the rearranged equation is 3, and the y-intercept is indeed (0, -10). Both points (0, -10) and (1, -7) lie on the line described by the equation.

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