Question
This is a graph with the x-axis labeled from -5 to 5 and the y-axis labeled from -4 to 4.
There is a diagonal line that passes through the following points:
(0, 4) (the y-intercept)
(2, 2)
(4, 0)
The line slopes downward from left to right, indicating a negative slope.
a) What is the slope of the graph? 3/2, -2/3, 2, -3,2
b) What is the y-intercept? 0,2, 0,4, 3,0
c) What is the equation of the line? y = -2/3x + 4, y = 3/2x + 4, y = -2x + 2, y = -3/2 + 3
There is a diagonal line that passes through the following points:
(0, 4) (the y-intercept)
(2, 2)
(4, 0)
The line slopes downward from left to right, indicating a negative slope.
a) What is the slope of the graph? 3/2, -2/3, 2, -3,2
b) What is the y-intercept? 0,2, 0,4, 3,0
c) What is the equation of the line? y = -2/3x + 4, y = 3/2x + 4, y = -2x + 2, y = -3/2 + 3
Answers
GPT-4o mini
Let's go through each part step by step based on the points provided for the diagonal line:
### a) **What is the slope of the graph?**
To determine the slope (m) of a line, we can use the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (0, 4) and (4, 0):
1. Let (x1, y1) = (0, 4) and (x2, y2) = (4, 0).
2. Plugging in the values:
\[
m = \frac{0 - 4}{4 - 0} = \frac{-4}{4} = -1
\]
Now, let's also calculate the slope using another pair of points (0, 4) and (2, 2):
1. Using (0, 4) and (2, 2):
\[
m = \frac{2 - 4}{2 - 0} = \frac{-2}{2} = -1
\]
Both calculations indicate a negative slope. Therefore:
**The slope is -1.**
However, it seems none of the given choices directly correspond. But let's verify the list:
3/2, -2/3, 2, -3, 2. **None of these match.**
### b) **What is the y-intercept?**
The y-intercept is the value of y when x = 0. From the point (0, 4), we see that when x is 0, y is 4.
**The y-intercept is 4.**
From the options given: 0, 2, 0, 4, 3, 0, so the answer is:
**The y-intercept is 0, 4.**
### c) **What is the equation of the line?**
To find the equation of the line, we can use the slope-intercept form of the equation \(y = mx + b\), where m is the slope and b is the y-intercept.
We already saw that:
- Slope (m) = -1
- Y-intercept (b) = 4
Thus, the equation will be:
\[
y = -1x + 4 \text{ or } y = -x + 4
\]
None of the given options directly match this, but from the options provided:
- y = -2/3x + 4,
- y = 3/2x + 4,
- y = -2x + 2,
- y = -3/2 + 3.
**The equation of the line does not match any provided choices accurately. The correct equation is \(y = -x + 4\).**
### Summary of Answers
- a) The slope is **-1**.
- b) The y-intercept is **4**.
- c) The equation of the line is **not accurately represented in the options**, but it is \(y = -x + 4\).
### a) **What is the slope of the graph?**
To determine the slope (m) of a line, we can use the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (0, 4) and (4, 0):
1. Let (x1, y1) = (0, 4) and (x2, y2) = (4, 0).
2. Plugging in the values:
\[
m = \frac{0 - 4}{4 - 0} = \frac{-4}{4} = -1
\]
Now, let's also calculate the slope using another pair of points (0, 4) and (2, 2):
1. Using (0, 4) and (2, 2):
\[
m = \frac{2 - 4}{2 - 0} = \frac{-2}{2} = -1
\]
Both calculations indicate a negative slope. Therefore:
**The slope is -1.**
However, it seems none of the given choices directly correspond. But let's verify the list:
3/2, -2/3, 2, -3, 2. **None of these match.**
### b) **What is the y-intercept?**
The y-intercept is the value of y when x = 0. From the point (0, 4), we see that when x is 0, y is 4.
**The y-intercept is 4.**
From the options given: 0, 2, 0, 4, 3, 0, so the answer is:
**The y-intercept is 0, 4.**
### c) **What is the equation of the line?**
To find the equation of the line, we can use the slope-intercept form of the equation \(y = mx + b\), where m is the slope and b is the y-intercept.
We already saw that:
- Slope (m) = -1
- Y-intercept (b) = 4
Thus, the equation will be:
\[
y = -1x + 4 \text{ or } y = -x + 4
\]
None of the given options directly match this, but from the options provided:
- y = -2/3x + 4,
- y = 3/2x + 4,
- y = -2x + 2,
- y = -3/2 + 3.
**The equation of the line does not match any provided choices accurately. The correct equation is \(y = -x + 4\).**
### Summary of Answers
- a) The slope is **-1**.
- b) The y-intercept is **4**.
- c) The equation of the line is **not accurately represented in the options**, but it is \(y = -x + 4\).