Question

8. a. Convert the following equation from point-slope form to standard form. y=2/5 (x-10) -3 b. Convert the following equation from standard form to slope-intercept form. 3x - 8y=12

Answer 1

Part a

we have the equation

$y=\frac{2}{5}(x-10)-3$

the standard form is

Ax+By=C

where

A is a positive integer

B and C are integers

so

apply distributive property

$\begin{gathered} y=(\frac{2}{5}x-\frac{2}{5}_{}\cdot10)-3 \\ y=\frac{2}{5}x-7 \end{gathered}$

Multiply both sides by 5

5y=2x-35

2x-5y=35 -------> standard form

Part b

we have the equation

3x-8y=12

the slope-intercept form is equal to

y=mx+b

so

isolate the variable y

8y=3x-12

divide by 8 on both sides

y=(3/8)x-12/8

simplify

y=(3/8)x-3/2