Question

Match the given information with the equation for the line.
A line that has a slope of 5/3 and a y-intercept of -4.
A line that contains the points (0,-2) and (4,0).
A line that contains the point (0,-8) with a slope of 3/2
A line that contains the y-intercept (0,-2) and a slope of -3/4

y=-3/4x-2
2y-x=-4
-5x+3y=-12
y=3/2x-8

Answer 1

Let's match each given line description with the appropriate equation:

1. **A line that has a slope of \(\frac{5}{3}\) and a y-intercept of -4.**
The equation of a line in slope-intercept form is \(y = mx + b\).
Here, \(m = \frac{5}{3}\) and \(b = -4\).
Therefore, the equation is:
\(y = \frac{5}{3}x - 4\).
(This equation is not in the provided options.)

2. **A line that contains the points (0,-2) and (4,0).**
First, we can find the slope using the points:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{4 - 0} = \frac{2}{4} = \frac{1}{2}.
\]
Since it goes through (0, -2), we can use the point-slope formula to write the equation:
\[
y + 2 = \frac{1}{2}(x - 0) \implies y = \frac{1}{2}x - 2.
\]
Checking the options,
let's re-examine:
The equation \(2y - x = -4\) can be rearranged:
\[
2y = x - 4 \implies y = \frac{1}{2}x - 2.
\]
So, this matches.

3. **A line that contains the point (0,-8) with a slope of \(\frac{3}{2}\).**
The equation in slope-intercept form will be:
\[
y = \frac{3}{2}x - 8.
\]
This matches with the option:
\(y = \frac{3}{2}x - 8\).

4. **A line that contains the y-intercept (0,-2) and a slope of -\(\frac{3}{4}\).**
The equation in slope-intercept form will be:
\[
y = -\frac{3}{4}x - 2.
\]
This matches with the equation \(y = -\frac{3}{4}x - 2\).

### Summary of Matches:
- A line that has a slope of \(\frac{5}{3}\) and a y-intercept of -4: No match in the options.
- A line that contains the points (0,-2) and (4,0): **\(2y - x = -4\)**
- A line that contains the point (0,-8) with a slope of \(\frac{3}{2}\): **\(y = \frac{3}{2}x - 8\)**
- A line that contains the y-intercept (0,-2) and a slope of -\(\frac{3}{4}\): **\(y = -\frac{3}{4}x - 2\)**