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= 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 find the equations of lines J, K, and L in the form \(y = mx + b\), we can follow these steps:

### Line J
Line J passes through 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. **Use point-slope form** to find the y-intercept (b). Using point \(a(0, 8)\):
\[
y = mx + b \implies 8 = \frac{-8}{3}(0) + b \implies b = 8
\]

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

### Line K
Line K passes through points \(e(5, -5)\) and \(f(0, -3)\).

1. **Calculate the slope (m)**:
\[
m = \frac{-3 - (-5)}{0 - 5} = \frac{2}{-5} = \frac{-2}{5}
\]

2. **Use point-slope form** to find the y-intercept (b). Using point \(f(0, -3)\):
\[
y = mx + b \implies -3 = \frac{-2}{5}(0) + b \implies b = -3
\]

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

### Line L
Line L passes through points \(c(-7, 0)\) and \(D(0, 3)\).

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

2. **Use point-slope form** to find the y-intercept (b). Using point \(D(0, 3)\):
\[
y = mx + b \implies 3 = \frac{3}{7}(0) + b \implies b = 3
\]

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

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