match the givin information with the equation for the line. a line that contains the y intercept (0,-2) and the slope of -3/4. a line that contains the pount (0.-8) with a slipe of 3/2. 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)

Answer 1

We can use the point-slope form of a line or the slope-intercept form to derive the equations based on the provided information. The slope-intercept form of a line is given by the equation:

\[ y = mx + b \]

where \( m \) is the slope and \( b \) is the y-intercept.

Now let's derive the equations based on the information given:

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

   • The y-intercept is \( b = -2 \) and the slope \( m = -3/4 \).
   • The equation is:
     \[ y = -\frac{3}{4}x - 2 \]

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

   • The y-intercept is \( b = -8 \) and the slope \( m = 3/2 \).
   • The equation is:
     \[ y = \frac{3}{2}x - 8 \]

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

   • Here, the slope \( m = 5/3 \) and the y-intercept \( b = -4 \).
   • The equation is:
     \[ y = \frac{5}{3}x - 4 \]

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

   • We can calculate the slope \( m \) using the formula:
     \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{4 - 0} = \frac{2}{4} = \frac{1}{2} \]
   • Since it passes through (0, -2), we can use the y-intercept \( b = -2 \).
   • The equation is:
     \[ y = \frac{1}{2}x - 2 \]

To summarize the equations:

1. \( y = -\frac{3}{4}x - 2 \)
2. \( y = \frac{3}{2}x - 8 \)
3. \( y = \frac{5}{3}x - 4 \)
4. \( y = \frac{1}{2}x - 2 \)