Question

Match the given information with the equation for the line.(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
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 y-intercept (0, -2) and a slope of −3/4
A line that contains the point (0, -8) with a slope of 3/2

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

Answer 1

To match the given information with the equations for the line, we analyze each statement and find the corresponding equation:

1. **A line that has a slope of 5/3 and a y-intercept of -4.**
- The slope-intercept form is \(y = mx + b\)
- Here, \(m = \frac{5}{3}\) and \(b = -4\).
- So, the equation is \(y = \frac{5}{3}x - 4\).
- **Response: None of the given options match this description.**

2. **A line that contains the points (0, -2) and (4, 0).**
- To find the slope, \(\frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{4 - 0} = \frac{2}{4} = \frac{1}{2}\).
- The y-intercept is \(-2\) (since it passes through (0, -2)).
- The equation is \(y = \frac{1}{2}x - 2\).
- **Response: None of the given options match this description.**

3. **A line that contains the y-intercept (0, -2) and a slope of −3/4.**
- This is already in slope-intercept form where \(b = -2\) and \(m = -\frac{3}{4}\).
- The equation is \(y = -\frac{3}{4}x - 2\).
- **Response: y = -3/4x - 2.**

4. **A line that contains the point (0, -8) with a slope of 3/2.**
- Again using the slope-intercept form \(y = mx + b\) where \(b = -8\) and \(m = \frac{3}{2}\).
- The equation is \(y = \frac{3}{2}x - 8\).
- **Response: y = 3/2x - 8.**

Now, let's summarize the correct matching:

1. None of the options match (slope = 5/3, y-intercept = -4)
2. None of the options match (points (0, -2) and (4, 0))
3. Match: **y = -3/4x - 2**
4. Match: **y = 3/2x - 8**

If restricted to given equations, the final matches are as follows:

- **A line that has a slope of 5/3 and a y-intercept of -4:** None match.
- **A line that contains the points (0, -2) and (4, 0):** None match.
- **A line that contains the y-intercept (0, -2) and a slope of −3/4:** **y = -3/4x - 2**
- **A line that contains the point (0, -8) with a slope of 3/2:** **y = 3/2x - 8**