Question

Express the first equation in slope intercept form simplify your answer

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the standard form for slope-intercept form for an equation of a line

$\begin{gathered} y=mx+b \\ m\text{ is the slope and b is the y-intercept} \end{gathered}$

STEP 2: Write the first given equation

$3-\frac{5y-x}{2}=2x+2$

STEP 3: Simplify further to get the slope intercept form

$\begin{gathered} \mathrm{Subtract\:}3\mathrm{\:from\:both\:sides} \\ 3-\frac{5y-x}{2}-3=2x+2-3 \\ -\frac{5y-x}{2}=2x-1 \\ \mathrm{Multiply\:both\:sides\:by\:}2 \\ 2\left(-\frac{5y-x}{2}\right)=2\cdot \:2x-2\cdot \:1 \\ -5y+x=4x-2 \\ 5y+x-x=4x-2-x \\ -5y=3x-2 \\ \mathrm{Divide\:both\:sides\:by\:}-5 \\ \frac{-5y}{-5}=\frac{3x}{-5}-\frac{2}{-5} \\ y=-\frac{3x-2}{5} \\ \\ Putting\text{ ina slope-intercept form will give:} \\ y=-\frac{3x}{5}+\frac{2}{5} \end{gathered}$

Hence, the answer is given as:

$y=-\frac{3}{5}x+\frac{2}{5}$