Question

Write an equation in slope-intercept form that is perpendicular to 4x - 5y = 1 and passes through (-3, 4).

Answer 1

y=
`(-5)/(4)`x +
`(-1)/( 4)`

Explanation:

4x-1=5y
4/5 is the original slope and negative
`(5)/(4)` is the perpendicular slope.
Using that to put (-3,4) and the slope into point-slope form:
y-4=
`(-5)/(4)`(x+3)
distribute and isolate y

y=
`(-5)/(4)`x +
`(-1)/(4)`

Answer 2

y = -5/4x + 1/4

Explanation:

*Pependicular line have negative reciprocal slopes*

Rewrite your equation to slope-intercept form: y = mx + b

y = mx + b

• m = slope
• b = y-intercept (when x = 0)

4x - 5y = 1 <== subtract 4x from both sides

-4x -4x

-5y = -4x + 1 <== divide both sides by -5

/-5 /-5

y = 4/5x - 1/5

Find the Negative reciprocal of the line:

Steps:

1. Take your original slope (4/5)

2. Flip it (5/4)

3. Change the sign (-5/4)

The slope of the perpendicular line would be: -5/4 (y = -5/4x + b)

We need to find the y-intercept (b) for the perpendicular line using (-3, 4):

y = -5/4x + b <== substitue -3 for x and 4 for y

4 = -5/4(-3) + b

4 = 15/4 + b <== multiplify both sides by 4

4(4 = 15/4 + b)

16 = 15 + 4b <== subtract 15 from both sides

-15 -15

1 = 4b <== divide both sides by 4

/4 /4

1/4 = b

y = -5/4x + b changes to y = -5/4x + 1/4

Hope this helps!