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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)
.

1 answer

To determine if the graph corresponds to the equation \(3x - y = 10\), we need to analyze the equation and its properties.

First, we can rearrange the equation into slope-intercept form (\(y = mx + b\)):

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

From this rearrangement, 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 analyze the graph based on the information provided. The line is described as upward slanting and passes through the point \((0, -10)\). This suggests a positive slope.

However, a slope of \(3\) means the line should rise steeply, not fall, which contradicts the descriptions about it having a slope of \(-3\).

Given that the graph is described as upward slanting and passes through \((0, -10)\), it indeed corresponds to a line with a positive slope, which is consistent with a slope of \(3\).

Thus, we conclude the following:

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

This would be the appropriate response since the graph would not represent the equation \(3x - y = 10\) if the slope is interpreted as negative (\(-3\)).