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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)

Sagot :

[tex]y=\frac{7}{8}x+\frac{57}{8}[/tex]

Explanation

Step 1

find the slope of the given line

[tex]y=\frac{7}{8}x+8[/tex]

this equation is in the form, slope -intercept

[tex]y=mx+b[/tex]

where m is the slope , so

[tex]\begin{gathered} y=\frac{7}{8}x+8\Rightarrow y=\text{ mx+b} \\ hence \\ m=slope=\frac{7}{8} \end{gathered}[/tex]

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

[tex]\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}[/tex]

then

Let

P1=C=(1,8)

slope=7/8

now, replace

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

I hope this helps you

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