Ask a New Question
Menu

.

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 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 whether the line shown is the correct representation of the equation \(3x - y = 10\), we need to check the slope and y-intercept of the line defined by that equation.

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

    From this we can see that:

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

  2. Analyzing the plotted points:

    • The points given in the illustration are \((0, 10)\) and \((1, -7)\).
    • The point \((0, 10)\) indicates the line crosses the y-axis at \(y = 10\) instead of \(y = -10\).

  3. Since the y-intercept of the line graphed is \( (0, 10) \) rather than \( (0, -10) \), and the slope indicated by the points is not consistent with the slope from the equation, we conclude:

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

This aligns with one of the provided response options but clarifies that the graph does not accurately represent \(3x - y = 10\).