Question

Write the equation of the graph in the form of
𝑦
=
𝑚
𝑥
+
𝑏
y=mx+b that matches. Click Here for Help Video.



Line J


𝑦
=
y=

𝑥

+
x +




Line K

𝑦
=
y=

𝑥
+
x+




Line L



𝑦
=
y=

𝑥
+
x+




line L has
c=-7,0 and
D=0,3

like k has
e=-5,-5
f=0,-3

line j has
a=0,8
b=3,0

Answer 1

To write the equations of lines J, K, and L in the slope-intercept form \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \) from the given coordinates.

### Line J:
Points: A(0, 8) and B(3, 0)

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

2. **Find the y-intercept \( b \)**:
Using point A(0, 8), since the y-intercept occurs when \( x = 0 \):
\[
b = 8
\]

So the equation of Line J is:
\[
y = -\frac{8}{3}x + 8
\]

### Line K:
Points: E(-5, -5) and F(0, -3)

1. **Find the slope \( m \)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - (-5)}{0 - (-5)} = \frac{-3 + 5}{0 + 5} = \frac{2}{5}
\]

2. **Find the y-intercept \( b \)**:
Using point F(0, -3):
\[
b = -3
\]

So, the equation of Line K is:
\[
y = \frac{2}{5}x - 3
\]

### Line L:
Points: C(-7, 0) and D(0, 3)

1. **Find the slope \( m \)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 0}{0 - (-7)} = \frac{3}{7}
\]

2. **Find the y-intercept \( b \)**:
Using point D(0, 3):
\[
b = 3
\]

So, the equation of Line L is:
\[
y = \frac{3}{7}x + 3
\]

### Summary:
- **Line J**: \( y = -\frac{8}{3}x + 8 \)
- **Line K**: \( y = \frac{2}{5}x - 3 \)
- **Line L**: \( y = \frac{3}{7}x + 3 \)