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

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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

1 answer

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!