Question

Question

Use the image to answer the question.

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 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)
.
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 .
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Answer 1

To determine if the graph represents the equation \(3x - y = 10\), we first need to rewrite the equation in slope-intercept form \(y = mx + b\).

Starting with the original equation:

\[3x - y = 10\]

We can rearrange it to solve for \(y\):

\[-y = -3x + 10\]

Now, multiplying by -1 gives us:

\[y = 3x - 10\]

From this, we can observe that:

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

Considering the information provided in the image, the upward slanting line goes through the point (0, -10) (which matches our y-intercept), but the slope of the line is also referenced.

Since the slope of the line we derived is 3 (not -3), we can conclude that the upward slanting line is indeed correct in the orientation but fails because it represents a different slope.

Thus, the correct statement is:

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