Question

Write the equation of a line that is perpendicular to y=2/7x +9 and that passes through the point (4,-6).

Answer 1

`y=-(7)/(2)x+8`

Explanation:

Given the equation

`y\:=\:(2)/(7)x+9`

comparing the equation with the slope-intercept form

`y =mx+b`

Here,

• m is the slope

• y is the intercept

so the slope of the line is 2/7

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so

the slope of the perpendicular line will be: -7/2

Therefore, the point-slope form of the equation of the perpendicular line that goes through (4,-6) is:

`y-y_1=m\left(x-x_1\right)`

`y-\left(-6\right)=(-7)/(2)\left(x-4\right)`

`y+6=(-7)/(2)\left(x-4\right)`

`y+6-6=(-7)/(2)\left(x-4\right)-6`

`y=-(7)/(2)x+8`