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.

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

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 .

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)
.

GPT-4o mini · Answer

To determine if the line graphed is the correct representation of the equation \(3x − y = 10\), we can find the slope and y-intercept of the equation.

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

From this, we can see that the slope \(m\) is 3 and the y-intercept \(b\) is -10, which corresponds to the point (0, -10).

Analyzing the graph:
- The closed points given are \((0, -10)\) and \((1, -7)\).
- The slope between these points can be calculated as: \[ \text{slope} = \frac{-7 - (-10)}{1 - 0} = \frac{3}{1} = 3 \] This matches the slope from the equation, which confirms that the line has the correct slope.

Since the slope is positive 3 and the y-intercept is (0, -10), the correct response based on the choices provided is:

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