Write the equation of the graph in the form of

Question

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

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=
y=

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+
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: \(y = \frac{3}{7}x + 3\)