Question

writr the equation of the line passing through the given point and satisfying the given condition give the equation (a) in the slope intercept form and (b) in a standard . (-8, -8); parrallel to -x+8y=32 simplify your answer

Answer 1

Step 1

Given;

$\begin{gathered} Points(-8,-8) \\ Equation\text{ line is parallel to -x+8y=32} \end{gathered}$

Step 2

A) For parallel lines the slopes are the same

$\begin{gathered} slope\text{ of given line will be;} \\ 8y=32+x \\ y=\frac{32+x}{8} \\ y=4+\frac{x}{8} \\ Slope,\text{ m=}\frac{1}{8} \end{gathered}$

From the given points the equation of the required line in slope-intercept form is;

$\begin{gathered} y=\frac{1}{8}x+b \\ -8=\frac{1}{8}(-8)+b \\ -8=-1+b \\ b=-8+1 \\ b=-7 \\ The\text{ equation in slope-intercept form is; y=}\frac{1}{8}x-7 \end{gathered}$

B) In standard form, the equation will be;

$\begin{gathered} y=\frac{1}{8}x-7 \\ 8y=8(\frac{1}{8}x)-7(8) \\ 8y=x-56 \\ 56=x-8y \\ Hence;\text{ x-8y=56} \end{gathered}$

Answers;

$\begin{gathered} \text{ A\rparen y=}\frac{1}{8}x-7 \\ B)x-8y=56 \end{gathered}$