Match the given with the equation for the line.(4 points) Put responses in the correct input to information 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 point (0, -8) with a slope of 32 A line that contains the points (0, -2) and (4, 0). A line that contains the y-intercept (0, -2) and a slope of −34

To match each description with the correct equation of the line, let's analyze each line given in the question.

1. A line that has a slope of 5/3 and a y-intercept of -4.

   • This can be written in slope-intercept form: \(y = mx + b\) → \(y = \frac{5}{3}x - 4\).
   • However, none of the given equations match this directly.

2. A line that contains the point (0, -8) with a slope of 32.

   • Again, using the slope-intercept form: \(y = mx + b\) → \(y = 32x - 8\).
   • None of the options match this equation either.

3. A line that contains the points (0, -2) and (4, 0).

   • The slope \(m\) between these points can be calculated as: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{4 - 0} = \frac{2}{4} = \frac{1}{2}. \]
   • The y-intercept is -2, thus the line can be written as: \[ y = \frac{1}{2}x - 2. \]
   • This does not match any options either.

4. A line that contains the y-intercept (0, -2) and a slope of −34.

   • This can be expressed in the slope-intercept form as: \[ y = -34x - 2. \]
   • Again, this does not match.

Now let's evaluate the given equations from the answers:

• Option 1: \( y = -\frac{3}{4}x - 2 \)
• Option 2: \( -5 + 3y = -12 \)
• Option 3: \( y = \frac{3}{2}x - 8 \)
• Option 4: \( 2y - x = -4 \)

Rearranging these equations to isolate y to evaluate matches:

1. \( y = -\frac{3}{4}x - 2 \)
2. Rearranging \( -5 + 3y = -12 \) we get \( 3y = -7 \rightarrow y = -\frac{7}{3} \quad \text{(Not a match)} \)
3. \( y = \frac{3}{2}x - 8 \)
4. Rearranging \( 2y - x = -4 \): \( 2y = x - 4 \rightarrow y = \frac{1}{2}x - 2 \quad \text{(Matches 3)}\)

Now we can match:

1. A slope of 5/3 and y-intercept of -4 → does not match any equations.
2. A point (0, -8) with slope of 32 → does not match either.
3. (0, -2) and (4, 0) → matched with → \( 2y - x = -4\) (which can be confirmed again to be slope \( \frac{1}{2} \)).
4. (0, -2) and slope of −34 → does not match any given equation.

So, based on accuracy let's collate:

1. Line with slope 5/3, y-intercept -4 → Not possible.
2. Line through (0, -8) with slope 32 → Not possible.
3. Line inter / slope from required points → Matches as \(2y - x = -4\).
4. Last one (-34 steep) → incorrect interpretation, returns to evaluate.

If exact matches can't apply - clearer entries must be updated; please confirm points or assist more accurately for further input.