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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
3
x
−
y
=
10
?

(1 point)
Responses

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

−
10
)
.

1 answer

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

First, let's rewrite the equation in slope-intercept form \(y = mx + b\):

Starting with: \[ 3x - y = 10 \]

Rearranging gives: \[ -y = -3x + 10 \] \[ y = 3x - 10 \]

From this equation, we can identify:

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

Now, let's analyze the points on the graph:

  • The points provided are \((0, -10)\) and \((1, -7)\).
  • We can calculate the slope between these two points.

The slope \(m\) is calculated as follows: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-7 - (-10)}{1 - 0} = \frac{-7 + 10}{1} = \frac{3}{1} = 3 \]

The computed slope of the line is indeed \(3\), and we confirmed that the y-intercept is \((0, -10)\).

Thus, based on this information, the correct response is:

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