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

Question

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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 y-intercept (0, -2) and a slope of −34
A line that contains the points (0, -2) and (4, 0).
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Answer 1

To match the given information with the equation for the line, we need to write the equations in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

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

   • Equation: \( y = 53x - 4 \)

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

   • Since the point is (0, -8), this means the y-intercept \( b = -8 \).
   • Equation: \( y = 32x - 8 \)

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

   • Given the y-intercept \( b = -2 \) and slope \( m = -34 \).
   • Equation: \( y = -34x - 2 \)

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

   • Slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{4 - 0} = \frac{2}{4} = \frac{1}{2} \)
   • With the point (0, -2) as the y-intercept, the equation is:
   • Equation: \( y = \frac{1}{2}x - 2 \)

Now, summarizing the equations for each line:

1. y = 53x - 4
2. y = 32x - 8
3. y = -34x - 2
4. y = \frac{1}{2}x - 2

Use the above equations to match them to the descriptions given.