Match the given information with the equation for the line.

Question

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

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

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

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

Answer 1

Let's match each description with the corresponding equation of the line using the slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

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

   • Here, the slope \( m = -\frac{3}{4} \) and the y-intercept \( b = -2 \).
   • Equation: \( y = -\frac{3}{4}x - 2 \).

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

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

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

   • Here, the slope \( m = \frac{5}{3} \) and the y-intercept \( b = -4 \).
   • Equation: \( y = \frac{5}{3}x - 4 \).

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

   • The y-intercept is \( b = -8 \) (from the point (0, -8)).
   • The slope \( m = \frac{3}{2} \).
   • Equation: \( y = \frac{3}{2}x - 8 \).

Summary of Equations:

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

Answer 2

those are not answers i see its these

A. 2y- x = -4

B. y = 2/3x - 8

C. -5x + 3y = -12

D y= -3/4x -2

Answer 3

Thank you for providing the options for the equations. Let's match each description you provided earlier with the given equations A, B, C, and D.

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

   • This matches option D: \( y = -\frac{3}{4}x - 2 \).

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

   • We found the slope to be \( \frac{1}{2} \) and the y-intercept to be \( -2 \), which corresponds to:
     \[ y = \frac{1}{2}x - 2 \quad \text{(not in the options, but matches D's form with different parameters)}. \]
   • So, none of the provided options match this description.

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

   • Not directly visible in the options, but in slope-intercept form would look like \( y = \frac{5}{3}x - 4 \) (does not match any options).

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

   • This line in slope-intercept form would be \( y = \frac{3}{2}x - 8 \). This corresponds to option B: \( y = \frac{2}{3}x - 8 \) but was provided as 3/2 in the description.

Final Matches:

• A line that contains the y-intercept (0, -2) and a slope of −3/4: D. \( y = -\frac{3}{4}x - 2 \)
• A line that contains the points (0, -2) and (4, 0): None matches the options directly
• A line that has a slope of 5/3 and a y-intercept of -4: None matches the options directly
• A line that contains the point (0, -8) with a slope of 3/2: B (not an exact match; slope should indicate as 3/2) but based on your answers.

Thus, the only clear match is option D for the first description.