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

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

Answer 1

To match the given information with the equations for the line, we analyze each statement and find the corresponding equation:

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

   • The slope-intercept form is \(y = mx + b\)
   • Here, \(m = \frac{5}{3}\) and \(b = -4\).
   • So, the equation is \(y = \frac{5}{3}x - 4\).
   • Response: None of the given options match this description.

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

   • To find the slope, \(\frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{4 - 0} = \frac{2}{4} = \frac{1}{2}\).
   • The y-intercept is \(-2\) (since it passes through (0, -2)).
   • The equation is \(y = \frac{1}{2}x - 2\).
   • Response: None of the given options match this description.

3. A line that contains the y-intercept (0, -2) and a slope of −3/4.

   • This is already in slope-intercept form where \(b = -2\) and \(m = -\frac{3}{4}\).
   • The equation is \(y = -\frac{3}{4}x - 2\).
   • Response: y = -3/4x - 2.

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

   • Again using the slope-intercept form \(y = mx + b\) where \(b = -8\) and \(m = \frac{3}{2}\).
   • The equation is \(y = \frac{3}{2}x - 8\).
   • Response: y = 3/2x - 8.

Now, let's summarize the correct matching:

1. None of the options match (slope = 5/3, y-intercept = -4)
2. None of the options match (points (0, -2) and (4, 0))
3. Match: y = -3/4x - 2
4. Match: y = 3/2x - 8

If restricted to given equations, the final matches are as follows:

• A line that has a slope of 5/3 and a y-intercept of -4: None match.
• A line that contains the points (0, -2) and (4, 0): None match.
• A line that contains the y-intercept (0, -2) and a slope of −3/4: y = -3/4x - 2
• A line that contains the point (0, -8) with a slope of 3/2: y = 3/2x - 8