Question

Write the equation of the line through the given point . Use slope intercept form (-9,8) perpendicular to y =-6/5x-3

Answer 1

`y\text{ = }(5)/(6)x\text{ + }(31)/(2)`

Step-by-step explanation

We want to find the equation of the line that passes through (-9, 8) and is perpendicular to:

`y\text{ = -}(6)/(5)x\text{ - 3}`

The slope of a line perpendicular to another line is the negative inverse of the slope of the line it is perpendicular to.

The slope of the given line is -6/5.

This means that the slope of the line we need is:

`(5)/(6)`

Now, we can find the equation of the line by applying the point-slope method:

y - y1 = m(x - x1)

where (x1, y1) is the point the line passes through

m = slope of the line

Therefore, we have:

`\begin{gathered} y\text{ - 8 = }(5)/(6)(x\text{ - (-9))} \\ y\text{ - 8 = }(5)/(6)(x\text{ + 9)} \\ y\text{ - 8 = }(5)/(6)x+((5)/(6)\cdot\text{ 9)} \\ y\text{ - 8 = }(5)/(6)x\text{ +}(15)/(2) \\ y\text{ = }(5)/(6)x\text{ + }(15)/(2)\text{ + 8} \\ y\text{ = }(5)/(6)x\text{ + }(31)/(2) \end{gathered}`

That is the equation of the line.