Question

write an equation for the line parallel to the given line that contains CC(1,8); y= 7/8x+8y=(type your answer and slope intercept form. use integers or fractions for any numbers in the equation. simplify your answer)

Answer 1

`y=(7)/(8)x+(57)/(8)`

Step-by-step explanation

Step 1

find the slope of the given line

`y=(7)/(8)x+8`

this equation is in the form, slope -intercept

`y=mx+b`

where m is the slope , so

`\begin{gathered} y=(7)/(8)x+8\Rightarrow y=\text{ mx+b} \\ hence \\ m=slope=(7)/(8) \end{gathered}`

Step 2

2 lines are parallel if the slope is the same,so we are looking for a line with slope 7/8 and the point c(1,8) is part of the line

use

`\begin{gathered} y-y_1=m(x-x_1) \\ \text{where P1(x}_1,y_1)\text{ is a known point of the line} \end{gathered}`

then

Let

P1=C=(1,8)

slope=7/8

now, replace

`\begin{gathered} y-y_1=m(x-x_1) \\ y-8=(7)/(8)(x-1) \\ y-8=(7)/(8)x-(7)/(8) \\ \text{add 8 in both sides} \\ y-8+8=(7)/(8)x-(7)/(8)+8 \\ y=(7)/(8)x+(57)/(8) \end{gathered}`

I hope this helps you