Question
Graphing Linear Equations Online Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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Question
Graph the linear equation y=−6x−4
.(1 point)
Responses
A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.
The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 4 right parenthesis, and left parenthesis 1 comma negative 10 right parenthesis.
- image with description: A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 4 right parenthesis, and left parenthesis 1 comma negative 10 right parenthesis. - - no response given
An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma 2 right parenthesis.
- image with description: An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma 2 right parenthesis. - - no response given
An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 2 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.
- image with description: An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 2 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis. - - no response given
An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows on both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 3 comma 0 right parenthesis.
Answers
GPT-4o mini
To graph the linear equation \( y = -6x - 4 \), we can identify a couple of key points:
1. **Slope and y-intercept**: The equation is in slope-intercept form (\( y = mx + b \)), where \( m \) is the slope and \( b \) is the y-intercept. Here, the slope (\( m \)) is \(-6\) and the y-intercept (\( b \)) is \(-4\). This means the line crosses the y-axis at the point \( (0, -4) \).
2. **Finding another point**: To find another point, we can plug in a value for \( x \). For example, if \( x = 1 \):
\[
y = -6(1) - 4 = -6 - 4 = -10
\]
So, the point \( (1, -10) \) is also on the line.
Now we can check the provided options against this information:
- The first option includes the points \( (0, -4) \) and \( (1, -10) \), which matches our calculations.
- The other options don't match these points or depict a line with the correct slope.
Thus, the correct graph corresponds to the first option:
**Graph of the equation \( y = -6x - 4 \)**:
- It passes through the points \( (0, -4) \) and \( (1, -10) \).
- The line slopes downward, which is consistent with a negative slope of \(-6\) in the equation.
So the answer is the first option.
1. **Slope and y-intercept**: The equation is in slope-intercept form (\( y = mx + b \)), where \( m \) is the slope and \( b \) is the y-intercept. Here, the slope (\( m \)) is \(-6\) and the y-intercept (\( b \)) is \(-4\). This means the line crosses the y-axis at the point \( (0, -4) \).
2. **Finding another point**: To find another point, we can plug in a value for \( x \). For example, if \( x = 1 \):
\[
y = -6(1) - 4 = -6 - 4 = -10
\]
So, the point \( (1, -10) \) is also on the line.
Now we can check the provided options against this information:
- The first option includes the points \( (0, -4) \) and \( (1, -10) \), which matches our calculations.
- The other options don't match these points or depict a line with the correct slope.
Thus, the correct graph corresponds to the first option:
**Graph of the equation \( y = -6x - 4 \)**:
- It passes through the points \( (0, -4) \) and \( (1, -10) \).
- The line slopes downward, which is consistent with a negative slope of \(-6\) in the equation.
So the answer is the first option.