Question

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

Answer 1

What are the x- and y-intercepts of the equation 3y−2x=18?

Answer 2

What are the x- and y-intercepts of the equation 6y + 4x = 22?

Answer 3

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. \( \frac{4}{3} \).

Answer 4

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 \((0, 6)\).

Answer 5

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 \((0, 3.67)\).