Asked by Bornana
Because the x-intercept is 3 and the y-intercept is –4, the points (3, 0) and (0, –4) are on the line. What is the slope of the line?
A. −4/3
B. 4/3
C. 3/4
D. −3/4
A. −4/3
B. 4/3
C. 3/4
D. −3/4
Answers
Answered by
GPT-4o mini
To find the slope of a line given two points, we can use the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
In this case, we have the points (3, 0) and (0, -4). Let's assign:
- \((x_1, y_1) = (3, 0)\)
- \((x_2, y_2) = (0, -4)\)
Now, substitute the values into the slope formula:
\[
m = \frac{-4 - 0}{0 - 3}
\]
This simplifies to:
\[
m = \frac{-4}{-3} = \frac{4}{3}
\]
So the slope of the line is:
\[
\boxed{\frac{4}{3}}
\]
Thus, the correct answer is B. \( \frac{4}{3} \).
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
In this case, we have the points (3, 0) and (0, -4). Let's assign:
- \((x_1, y_1) = (3, 0)\)
- \((x_2, y_2) = (0, -4)\)
Now, substitute the values into the slope formula:
\[
m = \frac{-4 - 0}{0 - 3}
\]
This simplifies to:
\[
m = \frac{-4}{-3} = \frac{4}{3}
\]
So the slope of the line is:
\[
\boxed{\frac{4}{3}}
\]
Thus, the correct answer is B. \( \frac{4}{3} \).
Answered by
GPT-4o mini
To find the x- and y-intercepts of the equation \(3y - 2x = 18\), we can set \(y = 0\) to find the x-intercept, and set \(x = 0\) to find the y-intercept.
**Finding the x-intercept:**
Set \(y = 0\):
\[
3(0) - 2x = 18
\]
This simplifies to:
\[
-2x = 18
\]
Now, solve for \(x\):
\[
x = \frac{18}{-2} = -9
\]
So the x-intercept is \((-9, 0)\).
**Finding the y-intercept:**
Set \(x = 0\):
\[
3y - 2(0) = 18
\]
This simplifies to:
\[
3y = 18
\]
Now, solve for \(y\):
\[
y = \frac{18}{3} = 6
\]
So the y-intercept is \((0, 6)\).
**Summary:**
The x-intercept is \((-9, 0)\) and the y-intercept is \((0, 6)\).
**Finding the x-intercept:**
Set \(y = 0\):
\[
3(0) - 2x = 18
\]
This simplifies to:
\[
-2x = 18
\]
Now, solve for \(x\):
\[
x = \frac{18}{-2} = -9
\]
So the x-intercept is \((-9, 0)\).
**Finding the y-intercept:**
Set \(x = 0\):
\[
3y - 2(0) = 18
\]
This simplifies to:
\[
3y = 18
\]
Now, solve for \(y\):
\[
y = \frac{18}{3} = 6
\]
So the y-intercept is \((0, 6)\).
**Summary:**
The x-intercept is \((-9, 0)\) and the y-intercept is \((0, 6)\).
Answered by
GPT-4o mini
To find the x- and y-intercepts of the equation \(6y + 4x = 22\), we'll follow the method of setting one variable to zero to find the other.
**Finding the x-intercept:**
Set \(y = 0\):
\[
6(0) + 4x = 22
\]
This simplifies to:
\[
4x = 22
\]
Now, solve for \(x\):
\[
x = \frac{22}{4} = \frac{11}{2} = 5.5
\]
So the x-intercept is \(\left(\frac{11}{2}, 0\right)\) or \((5.5, 0)\).
**Finding the y-intercept:**
Set \(x = 0\):
\[
6y + 4(0) = 22
\]
This simplifies to:
\[
6y = 22
\]
Now, solve for \(y\):
\[
y = \frac{22}{6} = \frac{11}{3}
\]
So the y-intercept is \(\left(0, \frac{11}{3}\right)\) or \((0, 3.67)\) (approximately).
**Summary:**
- The x-intercept is \(\left(\frac{11}{2}, 0\right)\) or \((5.5, 0)\).
- The y-intercept is \(\left(0, \frac{11}{3}\right)\) or \((0, 3.67)\).
**Finding the x-intercept:**
Set \(y = 0\):
\[
6(0) + 4x = 22
\]
This simplifies to:
\[
4x = 22
\]
Now, solve for \(x\):
\[
x = \frac{22}{4} = \frac{11}{2} = 5.5
\]
So the x-intercept is \(\left(\frac{11}{2}, 0\right)\) or \((5.5, 0)\).
**Finding the y-intercept:**
Set \(x = 0\):
\[
6y + 4(0) = 22
\]
This simplifies to:
\[
6y = 22
\]
Now, solve for \(y\):
\[
y = \frac{22}{6} = \frac{11}{3}
\]
So the y-intercept is \(\left(0, \frac{11}{3}\right)\) or \((0, 3.67)\) (approximately).
**Summary:**
- The x-intercept is \(\left(\frac{11}{2}, 0\right)\) or \((5.5, 0)\).
- The y-intercept is \(\left(0, \frac{11}{3}\right)\) or \((0, 3.67)\).