A1 4.3 Notes- Writing Equations Parallel/Perpendicular Lines

4.3 Writing Equations of Parallel and Perpendicular Lines

Objective: To recognize lines that are parallel and perpendicular

Warm-Ups

Multiple Choice

Write a point-slope form equation of the line containing the point (1,3) with a slope of 6

• $$y+1=-3\left(x-3\right)$$  

• $$y-3=6\left(x-1\right)$$  

• $$y-3=3\left(x-1\right)$$  

• $$y-1=6\left(x-3\right)$$  

Multiple Choice

Write an equation in slope-intercept form, using the equation

$$y+1=-\frac{3}{4}\left(x-4\right)$$  

• $$y=2x+\frac{3}{4}$$  

• $$y=\frac{3}{4}x+2$$  

• $$y=-2x+\frac{3}{4}$$  

• $$y=-\frac{3}{4}x+2$$  

In the coordinate plane, Parallel Lines have the SAME SLOPE, and will never intersect

Subject | Subject

Some text here about the topic of discussion

SLOPE of Parallel Lines

In the coordinate plane,

Parallel Lines have the SAME SLOPE

Multiple Select

Example 1) Which two lines are parallel?

• $$y=\frac{3}{7}x-25$$

• $$y=\frac{3}{7}x+2$$

• $$y=\frac{7}{3}x-25$$

• $$y=3x+13$$

• $$y=7x+9$$

Multiple Select

Example 2) Which two lines are parallel?

• $$y=-\frac{1}{4}x-25$$

• $$y=\frac{1}{4}x+2$$

• $$y=4x+13$$

• $$y=\frac{1}{4}x+9$$

​Example 3: Determine which lines are parallel

Multiple Choice

Are the two lines parallel?

• No

• Yes

Multiple Choice

Are the lines parallel?

• No

• Yes

​Example 4: Write an equation of the line that passes through (3,1) and is parallel to the line

​Example 4: Write an equation of the line that passes through (3,1) and is parallel to the line

​Example 4: Write an equation of the line that passes through (3,1) and is parallel to the line

Draw

Draw the equation in Point Slope Form

Multiple Choice

Example 4b) Write an equation of the line that passes through (3,1) and is parallel to the line y=2x+3

• y=-2x-5

• y=2x-5

• y=3x+5

• y=x-5

​In the coordinate plane two lines that intersect to form right angles are Perpendicular Lines

Perpendicular Lines have slopes that are OPPOSITE RECIPROCALS

Ex 4 and -¼ or -2 and ½

SLOPE of Perpendicular Lines

In the coordinate plane, Perpendicular Lines

have slopes that are OPPOSITE RECIPROCALS

Multiple Choice

What is the perpendicular slope of:  $$\frac{8}{5}$$  

• $$\frac{8}{5}$$  

• $$-\frac{8}{5}$$  

• $$-\frac{5}{8}$$  

• $$\frac{5}{8}$$  

Multiple Select

Example 5: Which two lines are perpendicular?

• $$y=\frac{3}{7}x-25$$

• $$y=-\frac{3}{7}x+2$$

• $$y=-\frac{7}{3}x-25$$

• $$y=3x+13$$

• $$y=7x+9$$

Multiple Choice

Example 6: Choose the equation that is perpendicular to the following line

$$y=-\frac{1}{4}x-1$$  

• $$y=-\frac{1}{4}x+5$$  

• $$y=\frac{1}{4}x-1$$  

• $$y=-4x-1$$  

• $$y=4x-3$$  

Multiple Choice

Write the equation of a line PERPENDICULAR to the line y = 3x + 2 that passes through the point (9, -2)

• y = -1/3x - 5

• y = 3x-29

• y = 1/3x -5

• y = -1/3x +1

Poll

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