Question

Match the given information with the equation for the line.

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

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 2

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 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.