Algebra Review for Units 3 and 4: Graphing Linear Equations and Inequalities

Critical Thinking Skill:Demonstrate Undestanding of Concepts

https://www.youtube.com/watch?v=_dqQb8iZtS4

Standard Form: Ax + By = C A, B and C must be integers and A>0

Slope-Intercept Form: y = mx + b

Point-Slope Form: (y - y1) = m(x - x1)

Graph using a tableex 1: y = -(2x + 3)

Graph using intercepts:ex 2: 2x + 5y = 10

Graph using slopeex 3: y = 2x + 2 3  

Graph:

x = 4

ex 5: y = x - 9 3  m =

 b =

Find the slope and y-intercept:

ex 6: 4x + 7y = 8

 m =

 b =

ex7: ( 3, 6) and ( 2, 0)

Find the slope using the formula:

ex8: ( 0, -2) and ( 2, y) m = 3

Solve for y:

State the domain and range for each relation. Is the relation a function?

ex 9: { ( 3, 4), (2, 3), (3, 6), (2, 0)}

ex 10: { ( 2, -1), (3, 0), (4, 6), (1, -3)}

ex 11: Look at the function that is graphed below.

0 5

y

x-5

-5

5

Which of these describe the range of this function?F.) y 0

G.) 0 y 5

H.) all real numbers

I.) All whole numbers

ex 12:If f(x) = x3 5x 2

find f(-2)

ex 13: Find the equation of the line with m = 5 going through point ( 4, 2). Use the slope-intercept formula.

ex 14: Find the equation of the line going through points ( 3, 4) and (5, 3). Use the point- slope formula.

Find the slopes of each line, and state whether the lines are parallel, perpendicular or neither.

ex 15). x + y = 6 and 8y - 12x - 12 = 0

-y < x + 5

ex 16: Graph

The table below shows the amount of water y in a tank after x minutes have elapsed.

minutes 2 4 6 8

gallons 80 60 40 20

a.) Write an equation to find the amount of water in gallons after the given number of minutes.

b.) Is water entering or leaving the tank?

c.) How much water is in the tank after 3 minutes?

d.) Find the slope and interpret its meaning.

e.) Find the x-intercept and y-intercept and interpret their meaning.