Question
se the image to answer the question.
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 3 right parenthesis, and left parenthesis 3 comma 2 right parenthesis.
Is this the correct graph of y=−13x+4
?(1 point)
Responses
Yes, it is the correct graph because this graph has a y
-intercept of (0,4)
.
Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 4 right parenthesis .
No, it is not the correct graph because this graph has a positive slope.
No, it is not the correct graph because this graph has a positive slope.
Yes, it is the correct graph because this graph has a y
-intercept of (0,3)
.
Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 3 right parenthesis .
No, it is not the correct graph because this graph used (0,3)
as the y
-intercept.
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 3 right parenthesis, and left parenthesis 3 comma 2 right parenthesis.
Is this the correct graph of y=−13x+4
?(1 point)
Responses
Yes, it is the correct graph because this graph has a y
-intercept of (0,4)
.
Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 4 right parenthesis .
No, it is not the correct graph because this graph has a positive slope.
No, it is not the correct graph because this graph has a positive slope.
Yes, it is the correct graph because this graph has a y
-intercept of (0,3)
.
Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 3 right parenthesis .
No, it is not the correct graph because this graph used (0,3)
as the y
-intercept.
Answers
GPT-4o mini
To determine whether the graph of the line with the given points (0, 3) and (3, 2) is the graph of the equation \( y = -13x + 4 \), we need to analyze the provided equation and the characteristics of the graph.
1. **Y-intercept:** The y-intercept of the equation \( y = -13x + 4 \) is \((0, 4)\).
2. **Slope:** The slope of this line is \(-13\), which is negative (indicating a downward slant).
Now let's analyze the points given:
- The point \((0, 3)\) indicates that when \(x = 0\), \(y = 3\).
- The point \((3, 2)\) indicates that when \(x = 3\), \(y = 2\).
Given these two points, we can find the slope between them:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 3}{3 - 0} = \frac{-1}{3}
\]
This slope is positive because the change in \(y\) is negative while the change in \(x\) is positive.
Since the graph with points \((0, 3)\) and \((3, 2)\) has a positive slope, it contradicts the negative slope of \( y = -13x + 4 \). Furthermore, the y-intercept of the graph shown is \((0, 3)\), not \((0, 4)\).
Therefore, the correct response is:
**No, it is not the correct graph because this graph has a positive slope.**
1. **Y-intercept:** The y-intercept of the equation \( y = -13x + 4 \) is \((0, 4)\).
2. **Slope:** The slope of this line is \(-13\), which is negative (indicating a downward slant).
Now let's analyze the points given:
- The point \((0, 3)\) indicates that when \(x = 0\), \(y = 3\).
- The point \((3, 2)\) indicates that when \(x = 3\), \(y = 2\).
Given these two points, we can find the slope between them:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 3}{3 - 0} = \frac{-1}{3}
\]
This slope is positive because the change in \(y\) is negative while the change in \(x\) is positive.
Since the graph with points \((0, 3)\) and \((3, 2)\) has a positive slope, it contradicts the negative slope of \( y = -13x + 4 \). Furthermore, the y-intercept of the graph shown is \((0, 3)\), not \((0, 4)\).
Therefore, the correct response is:
**No, it is not the correct graph because this graph has a positive slope.**