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.

Question

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 .

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 .

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

Answer 1

To determine if the graph represents the equation \( 3x - y = 10 \), we can rewrite the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

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

From this equation, we can see that:

• The slope (m) is 3
• The y-intercept (b) is -10, which corresponds to the point (0, -10).

Now, let's examine the points given in the illustration:

• The line passes through the points (0, -10) and (1, -7).

To check if these points are consistent with the slope calculated:

1. Calculate the change in y and the change in x between the points (0, -10) and (1, -7).
   • Change in y: -7 - (-10) = 3
   • Change in x: 1 - 0 = 1
   • Slope = change in y / change in x = 3 / 1 = 3

The slope observed from the two points is 3, which matches the slope of the equation.

Thus, the correct conclusion is:

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