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 contains the point (0, -8) with a slope of 32
A line that contains the y-intercept (0, -2) and a slope of −34
A line that has a slope of 53
and a y-intercept of -4.
A line that contains the points (0, -2) and (4, 0).

Answer 1

To match each piece of information with the corresponding equation of the line in slope-intercept form (y = mx + b), we can analyze each description and derive the equation based on the point and slope given.

1. **A line that contains the point (0, -8) with a slope of 32**:
- The y-intercept is -8 and the slope is 32.
- The equation is: **y = 32x - 8**

2. **A line that contains the y-intercept (0, -2) and a slope of −34**:
- The y-intercept is -2 and the slope is -34.
- The equation is: **y = -34x - 2**

3. **A line that has a slope of 53 and a y-intercept of -4**:
- The slope is 53 and the y-intercept is -4.
- The equation is: **y = 53x - 4**

4. **A line that contains the points (0, -2) and (4, 0)**:
- The y-intercept is -2 and the slope can be calculated as follows:
- Slope (m) = (y2 - y1) / (x2 - x1) = (0 - (-2)) / (4 - 0) = 2 / 4 = 1/2.
- Using the slope-intercept form with the y-intercept (-2), we get:
- The equation is: **y = (1/2)x - 2**

In summary, the corresponding equations for the lines are:
1. **y = 32x - 8**
2. **y = -34x - 2**
3. **y = 53x - 4**
4. **y = (1/2)x - 2**

You can insert these equations accordingly based on the points given in the original question.