Question

Write an equation of the line that passes through the given point: (3,2) y = -x+2

Answer 1

y = x-1 is equation of that is perpendicular to y = -x+2 and passes through (3,2)

Explanation:

We have given a point and equation of a line.

Let (x,y) = (3,2) and y= -x+2

y = mx+c is equation of line where m is slope and c is y-intercept.

Here, m = -1

Perpendicular lines have slopes negative reciprocals to each other.

so, the slope of perpendicular line is 1.

y = x+c is equation of lines that is perpendicular to y = -x+2.

Now , we have to find the y-intercept of above equation using given point.

2 = 3+c

c = -1

hence, y = x-1 is equation of that is perpendicular to y = -x+2 and passes through (3,2).

Answer 2

ANSWER

`y = x - 1`
EXPLANATION

We want to write an equation of the line that passes through the point


`(3,2)`
and perpendicular to


`y = - x + 2`

The slope of this line is -1.

The slope of the line perpendicular to this line is

`m = 1`
because the product of the two slopes should give us -1.


We now use the formula,



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

to find the required equation.


We substitute the values to obtain,



`y - 2 = 1(x - 3)`


`y - 2 = x - 3`



`y = x - 3 + 2`

This implies that,



`y = x - 1`