Match the given information with the equation for the line.(4 points)

Question

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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

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

EVERYTHING HAS A MATCH FIGURE IT THE HECK OUT DUMB BOT

Answer 1

Let's match the given lines with the corresponding equations based on the provided information.

1. A line that has a slope of 5/3 and a y-intercept of -4.
   The equation of the line in slope-intercept form (y = mx + b) is:
   $y=\frac{5}{3}x-4$
   None of the provided options match this equation.

2. A line that contains the points (0, -2) and (4, 0).
   The slope can be calculated using the formula $\text{slope}=\frac{y_2-y_1}{x_2-x_1}$:
   $\text{slope}=\frac{0-(-2)}{4-0}=\frac{2}{4}=\frac{1}{2}$
   The y-intercept (0, -2) can also be used with slope-intercept form:
   $y=\frac{1}{2}x-2$
   None of the provided options match this equation.

3. A line that contains the y-intercept (0, -2) and a slope of −3/4.
   Using the slope-intercept form again, we have:
   $y=-\frac{3}{4}x-2$
   None of the provided options match this equation.

4. A line that contains the point (0, -8) with a slope of 3/2
   The slope-intercept form gives us:
   $y=\frac{3}{2}x-8$
   This matches with the option: $y=3/2x-8$.

Now let's analyze the remaining equations to see if any can correspond to the other descriptions.

• $2y-x=-4$ can be rearranged to slope-intercept form. Rearranging gives:
  $2y=x-4\Rightarrow y=\frac{1}{2}x-2$
  This matches with the line that contains the points (0, -2) and (4, 0).

• $y=-\frac{3}{4}x-2$ doesn't match with any of the provided options but could fit for point 3 since the y-intercept is at (0, -2). However, the slope does not correctly match.

• For the equation $-5x+3y=-12$, rearranging:
  $3y=5x-12\Rightarrow y=\frac{5}{3}x-4$
  This matches line 1.

To summarize the matches:

1. A line that has a slope of 5/3 and a y-intercept of -4.
   Matched with -5x + 3y = -12.

2. A line that contains the points (0, -2) and (4, 0).
   Matched with 2y - x = -4.

3. A line that contains the y-intercept (0, -2) and a slope of −3/4.
   Matched with y = -3/4x - 2 (based on the description even if an option wasn't provided).

4. A line that contains the point (0, -8) with a slope of 3/2.
   Matched with y = 3/2x - 8.

Thank you for your patience!