Question
Graph the linear equation
y=23x−1
.
(1 point)
Responses
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 alt text: 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.
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 negative 2 comma negative 2 right parenthesis and left parenthesis 0 comma 1 right parenthesis.
Image with alt text: 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 negative 2 comma negative 2 right parenthesis and left parenthesis 0 comma 1 right parenthesis.
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 2 right parenthesis, and left parenthesis 1 comma negative 9 right parenthesis.
Image with alt text: 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 2 right parenthesis, and left parenthesis 1 comma negative 9 right parenthesis.
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 1 right parenthesis, and left parenthesis 3 comma 1 right parenthesis.
say if its first second third or fourth
y=23x−1
.
(1 point)
Responses
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 alt text: 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.
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 negative 2 comma negative 2 right parenthesis and left parenthesis 0 comma 1 right parenthesis.
Image with alt text: 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 negative 2 comma negative 2 right parenthesis and left parenthesis 0 comma 1 right parenthesis.
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 2 right parenthesis, and left parenthesis 1 comma negative 9 right parenthesis.
Image with alt text: 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 2 right parenthesis, and left parenthesis 1 comma negative 9 right parenthesis.
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 1 right parenthesis, and left parenthesis 3 comma 1 right parenthesis.
say if its first second third or fourth
Answers
GPT-4o mini
To determine which graph correctly represents the linear equation \(y = 23x - 1\), we can analyze the equation to find key points.
1. **Identify the y-intercept and slope**:
- The y-intercept occurs when \(x=0\):
\[
y = 23(0) - 1 = -1
\]
So, one point on the line is \((0, -1)\).
- The slope of the line is 23, meaning for every unit increase in \(x\), \(y\) increases by 23.
2. **Find another point using the slope**:
- If \(x = 1\):
\[
y = 23(1) - 1 = 22
\]
So, another point on the line is \((1, 22)\).
3. **Check which graph matches these points**:
- The first option does not match because it states the line passes through \((0, -4)\) and \((1, 2)\).
- The second option states it passes through \((-2, -2)\) and \((0, 1)\), which also does not match.
- The third option mentions points \((0, -2)\) and \((1, -9)\), which does not match.
- The fourth option mentions points \((0, -1)\) and \((3, 1)\), and the point \((0, -1)\) matches one of our results, but \((3, 1)\) does not match because at \(x=3\):
\[
y = 23(3) - 1 = 68
\]
Given the analysis, none of the presented options seem to accurately graph the line described by the equation \(y = 23x - 1\). However, the fourth option has one correct point \((0, -1)\), but due to changes in the second point, it remains misleading.
If you were looking for a point that best matches common linear graphing properties from your descriptions, you'd likely go with the fourth one.
1. **Identify the y-intercept and slope**:
- The y-intercept occurs when \(x=0\):
\[
y = 23(0) - 1 = -1
\]
So, one point on the line is \((0, -1)\).
- The slope of the line is 23, meaning for every unit increase in \(x\), \(y\) increases by 23.
2. **Find another point using the slope**:
- If \(x = 1\):
\[
y = 23(1) - 1 = 22
\]
So, another point on the line is \((1, 22)\).
3. **Check which graph matches these points**:
- The first option does not match because it states the line passes through \((0, -4)\) and \((1, 2)\).
- The second option states it passes through \((-2, -2)\) and \((0, 1)\), which also does not match.
- The third option mentions points \((0, -2)\) and \((1, -9)\), which does not match.
- The fourth option mentions points \((0, -1)\) and \((3, 1)\), and the point \((0, -1)\) matches one of our results, but \((3, 1)\) does not match because at \(x=3\):
\[
y = 23(3) - 1 = 68
\]
Given the analysis, none of the presented options seem to accurately graph the line described by the equation \(y = 23x - 1\). However, the fourth option has one correct point \((0, -1)\), but due to changes in the second point, it remains misleading.
If you were looking for a point that best matches common linear graphing properties from your descriptions, you'd likely go with the fourth one.