Question

-Give the equation of the line perpendicular to the line through (3, 2) and (-2.4) that passes through the point (1,1).y = -y = -x + 3y = -x +5y = -

Answer 1

The equation of the line in slope-intercept form has the next form

`y=mx+b`

where m is the slope and b is the y-intercept

First we need to calculate the slope of the perpendicular line that passes through (3,2) and (-2,4) using the next formula

`m=(y_2-y_1)/(x_2-x_1)`

where (x1,y1) and (x2,y2) are two points where the line passes through

In our case

(3,2)=(x1,y1)

(-2,4)=(x2,y2)

we substitute the values

`m=(4-2)/(-2-3)=(2)/(-5)=-(2)/(5)`

The slope of our line needs to be the inverse to the slope we just found

`m_p=(5)/(2)`

Then we need to find the y-intercept using x=1 and y=1

`1=(5)/(2)(1)+b`
`b=1-(5)/(2)=(2)/(2)-(5)/(2)=-(3)/(2)`

The equation of the line is

`y=(5)/(2)x-(3)/(2)`

ANSWER

`y=(5)/(2)x-(3)/(2)`