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 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). 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-intercept is (0, −10).
Answers
Answered by
GPT-4o mini
To determine whether the given graph represents the equation \( 3x - y = 10 \), we need to analyze the equation to find its slope and y-intercept.
Rearranging the equation \( 3x - y = 10 \) into slope-intercept form \( y = mx + b \):
1. Start with \( 3x - y = 10 \).
2. Rearranging gives \( -y = -3x + 10 \).
3. Multiplying everything by -1 gives \( y = 3x - 10 \).
From this form, we see:
- The slope \( m \) is \( 3 \).
- The y-intercept \( b \) is \( -10 \), which corresponds to the point \( (0, -10) \).
Next, let's consider the points given in the problem:
- One point is \( (0, -10) \), which confirms the y-intercept is correct.
- The second point is \( (1, -7) \). To check that this point lies on the line defined by the equation, substitute \( x = 1 \) into the equation:
\[
y = 3(1) - 10 = 3 - 10 = -7
\]
This shows that the point \( (1, -7) \) also satisfies the equation.
Since the line has a positive slope of \( 3 \) and the y-intercept is \( (0, -10) \), we conclude that the given graph is indeed the correct representation of the equation.
The correct response is:
**Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, −10).**
Rearranging the equation \( 3x - y = 10 \) into slope-intercept form \( y = mx + b \):
1. Start with \( 3x - y = 10 \).
2. Rearranging gives \( -y = -3x + 10 \).
3. Multiplying everything by -1 gives \( y = 3x - 10 \).
From this form, we see:
- The slope \( m \) is \( 3 \).
- The y-intercept \( b \) is \( -10 \), which corresponds to the point \( (0, -10) \).
Next, let's consider the points given in the problem:
- One point is \( (0, -10) \), which confirms the y-intercept is correct.
- The second point is \( (1, -7) \). To check that this point lies on the line defined by the equation, substitute \( x = 1 \) into the equation:
\[
y = 3(1) - 10 = 3 - 10 = -7
\]
This shows that the point \( (1, -7) \) also satisfies the equation.
Since the line has a positive slope of \( 3 \) and the y-intercept is \( (0, -10) \), we conclude that the given graph is indeed the correct representation of the equation.
The correct response is:
**Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, −10).**
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