Question

How do you find the equation of the line. write the equation in standard form. through (7,-5); parallel to the line 2x+9y=8

Answer 1

First, we need to clear y in the line given

`\begin{gathered} 2x+9y=8 \\ 9y=-2x+8 \\ y=-(2)/(9)x+(8)/(9) \end{gathered}`

because we need to have the slope-intercept form

`y=mx+b`

where m is the slope

if the line is parallel that have the same slope so the slope of the line that passes through (7,-5) is

m=-2/9

(7,-5)=(x1,y1)

In order to obtain the equation of the line

`y-y_1=m(x-x_1)`

then we substitute the values

`\begin{gathered} y+5=-(2)/(9)(x-7) \\ y+5=-(2)/(9)x+(14)/(9) \\ y=-(2)/(9)x-(31)/(9) \end{gathered}`

the equation of the line is

`y=-(2)/(9)x-(31)/(9)`