Question

Write the equation of the graph in the form of y=mx+b that matches.
line j is (3,0) and (0,8)
line k is (0,-3) and (-5,-4)
line l is (0,3) and (-7,0)

Answer 1

To write the equations of the lines \( j \), \( k \), and \( l \) in the form \( y = mx + b \), we need to find the slope (\( m \)) and y-intercept (\( b \)) for each line.

### Line j: Passing through points (3, 0) and (0, 8)

1. **Find the slope \( m \)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 0}{0 - 3} = \frac{8}{-3} = -\frac{8}{3}
\]

2. **Using point-slope form to find the equation**:
Using point (0, 8):
\[
y - 8 = -\frac{8}{3}(x - 0)
\]
\[
y = -\frac{8}{3}x + 8
\]

**Equation of line j**:
\[
y = -\frac{8}{3}x + 8
\]

---

### Line k: Passing through points (0, -3) and (-5, -4)

1. **Find the slope \( m \)**:
\[
m = \frac{-4 - (-3)}{-5 - 0} = \frac{-4 + 3}{-5} = \frac{-1}{-5} = \frac{1}{5}
\]

2. **Using point-slope form to find the equation**:
Using point (0, -3):
\[
y - (-3) = \frac{1}{5}(x - 0)
\]
\[
y + 3 = \frac{1}{5}x
\]
\[
y = \frac{1}{5}x - 3
\]

**Equation of line k**:
\[
y = \frac{1}{5}x - 3
\]

---

### Line l: Passing through points (0, 3) and (-7, 0)

1. **Find the slope \( m \)**:
\[
m = \frac{0 - 3}{-7 - 0} = \frac{-3}{-7} = \frac{3}{7}
\]

2. **Using point-slope form to find the equation**:
Using point (0, 3):
\[
y - 3 = \frac{3}{7}(x - 0)
\]
\[
y - 3 = \frac{3}{7}x
\]
\[
y = \frac{3}{7}x + 3
\]

**Equation of line l**:
\[
y = \frac{3}{7}x + 3
\]

---

### Summary of Equations
- Line j: \( y = -\frac{8}{3}x + 8 \)
- Line k: \( y = \frac{1}{5}x - 3 \)
- Line l: \( y = \frac{3}{7}x + 3 \)