Question

Express the first equation in slope intercept form simplify your answer

Answer 1

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-(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-(5y-x)/(2)-3=2x+2-3 \\ -(5y-x)/(2)=2x-1 \\ \mathrm{Multiply\:both\:sides\:by\:}2 \\ 2\left(-(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 \\ (-5y)/(-5)=(3x)/(-5)-(2)/(-5) \\ y=-(3x-2)/(5) \\ \\ Putting\text{ ina slope-intercept form will give:} \\ y=-(3x)/(5)+(2)/(5) \end{gathered}`

Hence, the answer is given as:

`y=-(3)/(5)x+(2)/(5)`