2.4 Parallel and Perpendicular Lines

point-slope form

How to write an equation of a line when you know the slope and at least one point on the line.

​To find the slope from a Standard Form Equation:

​

• ​Find the x-intercept and y-intercept. Then use a table or Desmos to find the slope between those two points.

• Example: 2x + 3y = 12

Multiple Choice

Find the slope.

• -2/3
• 2/3
• -3/2
• 3/2

y - y₁ = m(x - x₁)

Given: m= 2 and the line goes through (1, 6)

​Write the Point-Slope equation of the line​

​

m is your slope

1 is your x value

6 is your y value

​

​​

Plug in your values ---> y - 6 = 2(x - 1)

​Example:

Multiple Choice

Write an equation in point-slope form of the line that passes through the given point and has the given slope: (1, 3); m = 5

• y - 3 = 5 (x - 1)

• y - 1 = 5 ( x - 3)

• y + 3 = 5 (x + 1)

• y + 1 = 5 ( x + 3)

Multiple Choice

What is the slope-intercept form of this equation?

y – 3 = –2 (x + 4)

• y = -2x - 5

• y = -2x + 7

​2.4 Parallel and Perpendicular Lines

Different y-intercepts!

In the coordinate plane, Perpendicular Lines

have slopes that are OPPOSITE RECIPROCALS

Perpendicular Lines

Lines that intersect at a right (90 degree) angle

SLOPE of Perpendicular Lines

In the coordinate plane, Perpendicular Lines

have slopes that are OPPOSITE RECIPROCALS

Multiple Choice

What is the slope of a line perpendicular to -10/3

• -10/3

• 10/3

• 3/10

• -3/10

Multiple Choice

What slope is parallel to:  
m = 3/4

• 4/3
• 3/4
• -3/4
• -4/3

Multiple Choice

What is the slope of a line perpendicular to a line with slope ^-6/₅ ?

• ^-6/₅

• ^-5/6

• ⁵/₆

• ^-4/₃