Question

Write the equation of the line through the given point. Use slope-intercept form. (-5,2); perpendicular to y = - 2/3x +5

Answer 1

`y=(3)/(2)x+(19)/(2)`

Step-by-step explanation

Step 1

we have a perpendicular line, its slope is

`\begin{gathered} y=(-2)/(3)x+5 \\ \text{slope}=(-2)/(3) \end{gathered}`

two lines are perpendicular if

`\begin{gathered} \text{slope}1\cdot\text{ slope2 =-1} \\ \text{then} \\ \text{slope}1=\frac{-1}{\text{slope 2}} \end{gathered}`

replace

`\text{slope1}=((-1)/(1))/((-2)/(3))=(-3)/(-2)=(3)/(2)`

so, our slope is 3/2

Step 2

using slope=3/2 and P(-5,2) find the equation of the line

`\begin{gathered} y-y_0=m(x-x_0) \\ y-2=(3)/(2)(x-(-5)) \\ y-2=(3)/(2)(x+5) \\ y-2=(3)/(2)x+(15)/(2) \\ y=(3)/(2)x+(15)/(2)+2 \\ y=(3)/(2)x+(19)/(2) \end{gathered}`