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 find the equations of the lines in the form \(y = mx + b\) (slope-intercept form) for lines J, K, and L, we need to determine the slope (\(m\)) and the y-intercept (\(b\)) for each line based on the given points.

### Line J

Given points: \(A(0, 8)\) and \(B(3, 0)\)

First, we will calculate the slope \(m\) using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the points:
\[
m = \frac{0 - 8}{3 - 0} = \frac{-8}{3}
\]

Now, using the y-intercept where the line crosses the y-axis at point A (0, 8), we can write the equation:
\[
y = -\frac{8}{3}x + 8
\]

### Line K

Given points: \(E(5, -5)\) and \(F(0, -3)\)

Calculating the slope \(m\) using the same formula:
\[
m = \frac{-3 - (-5)}{0 - 5} = \frac{-3 + 5}{0 - 5} = \frac{2}{-5} = -\frac{2}{5}
\]

Using point F (0, -3) as the y-intercept:
\[
y = -\frac{2}{5}x - 3
\]

### Line L

Given points: \(C(-7, 0)\) and \(D(0, 3)\)

Calculating the slope \(m\):
\[
m = \frac{3 - 0}{0 - (-7)} = \frac{3}{7}
\]

Using point D (0, 3) as the y-intercept:
\[
y = \frac{3}{7}x + 3
\]

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