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 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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Answers
GPT-4o mini
To determine if the graph given corresponds to the equation \( 3x - y = 10 \), we can analyze the equation step by step.
First, let's rearrange the equation to slope-intercept form (\( y = mx + b \)), where \( m \) is the slope and \( b \) is the y-intercept.
Starting with the equation:
\[
3x - y = 10
\]
We can isolate \( y \):
\[
-y = -3x + 10
\]
\[
y = 3x - 10
\]
Now, we identify the slope and the y-intercept:
- The slope \( m \) is 3.
- The y-intercept \( b \) is -10, which corresponds to the point \( (0, -10) \).
Next, we can check the slope by examining one of the points given in the question. The graph describes points at \( (0, -10) \) (which is the y-intercept) and \( (1, -7) \).
Calculating the slope between these two points:
- The change in \( y \) (vertical change) from \(-10\) to \(-7\) is:
\[
-7 - (-10) = 3
\]
- The change in \( x \) (horizontal change) from \( 0 \) to \( 1 \) is:
\[
1 - 0 = 1
\]
The slope is given by the ratio of the vertical change to the horizontal change:
\[
\text{slope} = \frac{3}{1} = 3
\]
Since the slope is 3, and the y-intercept is indeed \( (0, -10) \), the correct conclusion is that the graph shown corresponds to the equation \( 3x - y = 10 \).
The correct response is:
**Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, -10).**
First, let's rearrange the equation to slope-intercept form (\( y = mx + b \)), where \( m \) is the slope and \( b \) is the y-intercept.
Starting with the equation:
\[
3x - y = 10
\]
We can isolate \( y \):
\[
-y = -3x + 10
\]
\[
y = 3x - 10
\]
Now, we identify the slope and the y-intercept:
- The slope \( m \) is 3.
- The y-intercept \( b \) is -10, which corresponds to the point \( (0, -10) \).
Next, we can check the slope by examining one of the points given in the question. The graph describes points at \( (0, -10) \) (which is the y-intercept) and \( (1, -7) \).
Calculating the slope between these two points:
- The change in \( y \) (vertical change) from \(-10\) to \(-7\) is:
\[
-7 - (-10) = 3
\]
- The change in \( x \) (horizontal change) from \( 0 \) to \( 1 \) is:
\[
1 - 0 = 1
\]
The slope is given by the ratio of the vertical change to the horizontal change:
\[
\text{slope} = \frac{3}{1} = 3
\]
Since the slope is 3, and the y-intercept is indeed \( (0, -10) \), the correct conclusion is that the graph shown corresponds to the equation \( 3x - y = 10 \).
The correct response is:
**Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, -10).**