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

Question

Put responses in the correct input to 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 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).
A line that has a slope of 53
and a y-intercept of -4.
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Answer 1

To match the given information with the equations for the lines, we can utilize the slope-intercept form of a line, which is given by the equation:

\[ y = mx + b \]

Where:

• \( m \) is the slope of the line.
• \( b \) is the y-intercept of the line.

Now, let's analyze each provided statement.

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

   • Here, the y-intercept \( b = -8 \) and the slope \( m = 32 \).
   • Equation: \( y = 32x - 8 \)

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

   • Here, \( b = -2 \) and \( m = -34 \).
   • Equation: \( y = -34x - 2 \)

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

   • The y-intercept \( b = -2 \). To find the slope, \( m \):
     • Slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{4 - 0} = \frac{2}{4} = \frac{1}{2} \)
   • Equation: \( y = \frac{1}{2}x - 2 \)

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

   • Here, \( b = -4 \) and \( m = 53 \).
   • Equation: \( y = 53x - 4 \)

Now we have the corresponding equations for each statement:

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

You can match them accordingly based on the information given.