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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)
.
Yes, it is the correct graph because the slope is 3 and the y -intercept is left parenthesis 0 comma negative 10 right parenthesis .
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1 answer

To determine if the given graph represents the equation \(3x - y = 10\), we first need to analyze the equation.

  1. Rearranging the equation to slope-intercept form (\(y = mx + b\)): \[ 3x - y = 10 \implies -y = -3x + 10 \implies y = 3x - 10 \]

This tells us:

  • The slope (\(m\)) is \(3\).
  • The y-intercept (\(b\)) is \(-10\), which means the line crosses the y-axis at the point \((0, -10)\).

  1. Next, we interpret the graph described in the question:

    • The line is upward slanting (which indicates a positive slope).
    • It passes through the points \((0, -10)\) and \((1, -7)\).

  2. Let's verify the slope between the two points:

    • The slope can be calculated using: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-7 - (-10)}{1 - 0} = \frac{-7 + 10}{1} = \frac{3}{1} = 3 \]

The calculated slope is \(3\), and the y-intercept is indeed \((0, -10)\), as given.

Considering all of this, the correct interpretation is: Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, −10).

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