Question

Find the equation of the line through (-1, 7) which is parallel to the line y=8x +4.

Answer 1

`y=8x+15`

Step-by-step explanation

Step 1

2 lines are parallel if they have the same slope, so

a) let's check the slope of the given line

`y=8x+4`

it is in the form

`\begin{gathered} y=mx+b,\text{ where m is the slope} \\ \text{hence, } \\ y=8x+4\rightarrow y=mx+b \\ m=8 \\ so \\ Slope_1_{}=\text{ 8} \end{gathered}`

so, the slope of the line we are looking for is 8

Step 2

Now, to find the equation of the line, we can use this expression

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

then, Let

`\begin{gathered} \text{ Slope}_2=8 \\ P(-1,7) \end{gathered}`

replace,

`\begin{gathered} y-y_1=m(x-x_1) \\ y-7=8(x-(-1)) \\ y-7=8(x+1) \\ y-7=8x+8 \\ \text{add 7 in both sides} \\ y-7+7=8x+8+7 \\ y=8x+15 \end{gathered}`

therefore, the answer is

`y=8x+15`

I hope this helps you