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 53 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

Let's match each line description to the corresponding equation.

1. A line that has a slope of 53 and a y-intercept of -4.

   • This line can be written in slope-intercept form as \( y = mx + b \), where \( m = 53 \) and \( b = -4 \).
   • None of the answer choices match this description.

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

   • This can also be represented in slope-intercept form. \( y = 32x - 8 \).
   • None of the answer choices match this description.

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

   • First, calculate the slope: \( m = \frac{0 - (-2)}{4 - 0} = \frac{2}{4} = \frac{1}{2} \).
   • Using the point (0, -2) as the y-intercept, the equation is \( y = \frac{1}{2}x - 2 \).
   • None of the answer choices match this description.

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

   • Using slope-intercept form, the equation is \( y = -34x - 2 \).
   • None of the answer choices match this description.

Now let's revisit the answer choices:

1. \(y = -\frac{3}{4}x - 2\)
2. \(-5 + 3y = -12\) \( \Rightarrow 3y = -7\) \( \Rightarrow y = -\frac{7}{3}\) (not a match)
3. \(y = \frac{3}{2}x - 8\)
4. \(2y - x = -4\) \( \Rightarrow 2y = x - 4\) \( \Rightarrow y = \frac{1}{2}x - 2\)

Based on modifications or reinterpretations of the options, we notice:

• \( 2y = x - 4 \) corresponds to the line through points (0, -2) and (4, 0) with slope equal to \( \frac{1}{2} \).
• \(y = -\frac{3}{4}x - 2\) does not match with any description. Similarly, the equation \(y = \frac{3}{2}x - 8\) does not fit the descriptions.

From the calculations, the only suitable matches based on the previously provided options yield:

1. A line with slope 53 isn't included
2. A line with point (0, -8) isn’t included
3. The correct response for a line from points (0, -2) and (4, 0) becomes \(2y - x = -4\)
4. The equation for the last point isn’t presented either.

Indeed, it’s clear that a perfect match isn't available from the given equations to their descriptions as expected based on the conventions of slope-intercept forms presented.

Are you seeking confirmation of these choices or further elaboration on constructing specific slope-intercept forms?