Linear Functions

Linear Functions Review

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Write a linear equation for two points

(1)Calculate the slope using m= (y2-y1)/(x2-x1).

(2)Substitute the slope and one of the points into the y=mx+b equation.

(3) Solve for b.

Video Review: https://tinyurl.com/y3qg7q8f

Multiple Choice

Write equation of the line containing (0,-3) and (4,1)

• y = 1x + 1

• y = 1x - 3

• y = -1x + 1

• y = -1x - 3

Multiple Choice

Find the equation of the line that passes through the points:

(-2, 4) and (1, 10)

• y = 2x - 1

• y = -2x + 1

• y = 2x

• y = -2x

Multiple Choice

What is the formula for slope-intercept form?

• ax + by = c
• y = mx
• ax = by
• y = mx + b

Writing a linear equation with a point and parallel line.

(1) Given y₁=m₁x₁ +b₁ and y2=m₂x₂ +b₂

(2) Identify slope of original line

(3) Substitute slope (m2) and point into the y=mx+b equation.

(4) Parallel Lines: m₂ =m₁

(5) Solve for b.

Video Resource: https://tinyurl.com/y48n7wka

Multiple Choice

write the equation of a line that is parallel to y = -7x + 5 and passes through the point (0, 6)

• y = -7x + 6

• y + 0 = -7(x - 6)

• y = 6

• y + 6 = -7(x - 0)

Multiple Choice

Write the equation of a line parallel to y = -1/2x + 3 and that goes through the point (4, -1)

• y + 1 = -1/2(x - 4)

• y - 1 = -1/2(x + 4)

• y + 1 = 2(x - 4)

• y - 1 = 2(x + 4)

Writing a linear equation with a point and Perpendicular line.

(1) Given y₁=m₁x₁ +b₁ and y2=m₂x₂ +b_2.

(2) Identify slope of original line Perpendicular lines : m₂ = - 1/m₁

(3) Substitute new slope (m2) and the point into the y=mx+b equation

(4) Solve for b.

Video Resource: https://tinyurl.com/y29ar84c

Multiple Choice

Are these lines parallel, perpendicular, or just intersecting (but not perpendicular)?

 $y=6x+2$  $y=-6x-2$   

• Parallel

• Perpendicular

• Intersecting (but not perpendicular)

Multiple Choice

Write the equation of a line PERPENDICULAR to  $y=\frac{1}{3}x-9$  that passes through the point (-6, 10).

•  $y=\frac{1}{3}x-9$ 

•  $y=\frac{1}{3}x+10$ 

•  $y=-3x+6$ 

•  $y=-3x-8$ 

Multiple Choice

Determine the equation of a line perpendicular to y=-3x-2 and going through the point (9, 2), in slope-intercept form.

• $y=\frac{1}{3}x-3$

• $y=-\frac{1}{3}x-9$

• $y=\frac{1}{3}x-1$

• $y=-3x-9$

Write a Linear Model

(1) Identify m. This is the rate of change indicated by key words such as per or each.

(2) Identify b. This is the initial or starting value. This may be a fee, flat rate, etc.

(3) Sometimes you will be given two points (two inputs and two results) and will need to calculate m and b yourself.

Video Resource: https://tinyurl.com/y6sddoa7

Multiple Choice

The local service center advertises that it charges a flat fee of $50 plus $8 per mile to tow a vehicle. Write an equation that represents the total cost (C) of a service for m miles of towing.

• y = 8x + 50

• C = 50m +8

• y = 50x + 8

• C = 8m + 50

Multiple Choice

The amusement park charges $20 to get in plus $1.50 per ride. Which linear equation below represents this relationship.

• y=1.5+20x

• y=1.5x + 20

• y = 20x + 1.5

• y= 21.5x

Solving Rational Expressions

(1) Find a common denominator.

(2) Determine the extraneous values (The values of x that would make the denominator equal to 0.)

(3) Multiply both sides of the equation by the denominator to eliminate it.

(4) Solve for x.

Video Resource: https://tinyurl.com/y5xfnjy9

Multiple Choice

Solve by cross-multiplying.

• x = -1, 5

• No Solution

• x = -4, 5

• x= -4

Multiple Choice

Solve and check for extraneous solutions

• x=5

• x= -5

• No Solution

Multiple Choice

Solve for r

• 5

• - 5, 4

• - 5

• 5, 4