Question

find the equation of the line passing through the given point and perpendicular to the given equation write your answer in slope intercept form

Answer 1

Slope-intercept form:

y = mx + b "m" is the slope, "b" is the y-intercept

For lines to be perpendicular, their slopes have to be the opposite/negative reciprocals (flipped sign and number)

For example:

slope is 2

perpendicular line's slope is -1/2

slope is -2/3

perpendicular line's slope is 3/2

3.) y = 2x - 2

The given line's slope is 2, so the perpendicular line's slope is -1/2

`y=-(1)/(2)x+b` To find "b", plug in the point (-5 , 5) into the equation

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

`5=(5)/(2)+b` Subtract 5/2 on both sides

`5-(5)/(2)=b` Make the denominators the same

`(10)/(2)-(5)/(2)=b`

`(5)/(2)=b`

`y=-(1)/(2)x+(5)/(2)`

4.) -6x + 5y = -10 Get "y" by itself, add 6x on both sides

5y = -10 + 6x Divide 5 on both sides

`y=-2+(6)/(5)x`

The given line's slope is 6/5, so the perpendicular line's slope is -5/6.

`y=-(5)/(6)x+b` Plug in (-2, 5)

`5 = -(5)/(6)(-2)+b`

`5=(10)/(6)+b\\ 5=(5)/(3)+b` Subtract 5/3 on both sides

`5-(5)/(3) =b` Make the denominators the same

`(15)/(3)-(5)/(3)=b\\(10)/(3) =b`

`y = -(5)/(6)x+(10)/(3)`

7.) Perpendicular line's slope is -2

y = -2x + b Plug in (1,4)

4 = -2(1) + b

4 = -2 + b

6 = b

y = -2x + 6

8.) Perpendicular line's slope is -1/4

`y = -(1)/(4)x+b` Plug in (-5 , 2)

`2=-(1)/(4)(-5)+b`

`2 = (5)/(4)+b` Subtract 5/4 on both sides

`2-(5)/(4)=b` Make the denominators the same

`(8)/(4)-(5)/(4)=b`

`(3)/(4)=b`

`y=-(1)/(4)x+(3)/(4)`