Algebra I Midterm Review

Algebra I Midterm Review

^{The following topics will be on the Midterm}

• Functions

• Linear Equations

• Slope and y-intercept

• Linear Inequalities

• Systems of Linear Equations

• Systems of Linear Inequalities

Functions

A function is when an input (x-value) is pair or mapped with one and only one output (y-value)

You could say a function is an X that equals one and only one Y.

Remember all functions is pass the vertical line test too.

Multiple Choice

Which table represents a linear function?

• Table A

• Table B

• Table C

• Table D

Multiple Choice

Which set of values is a function?

• (9,5) (10,5) (9,-5) (10,-5)

• (3,4) (4,-3) (7,4) (3, 8)

• (6,-5) (7, -3) (8, -1) (9, 1)

• (2, -2) (5, 9) (5, -7) (1, 4)

Multiple Choice

Determine which of the following relations is NOT a function.

• A non-vertical linear graph.

• A set of ordered pairs where an x term repeats.

• A set of ordered pairs where a y term repeats.

• A U-shaped graph.

Multiple Choice

Is the following mapping a function or a relation only?

• Function

• Relation Only

Multiple Choice

All of the y values or outputs are called what?

• Domain

• Range

• Relation

• Function

Multiple Choice

5. All of the x values or inputs are called what?

• Domain

• Range

• Relation

• Function

Multiple Choice

9. Is this graph a function or not a function?

• Function

• Not a function

Slope

• Slope is a ratio that describes the direction and steepness of a line.

• Slope compares a line's "rise" to its "run"

• Rise always refers to the vertical change (change in the y-value)

• Run always refers to the horizontal change (change in the x-value)

• It is represented in y=mx+b as the M-value

Calculating Slope from a graph

Remember to always write a ratio where the rise is over the run.

Multiple Choice

Find the slope of the line.

• -5/4

• -4/5

• 5/4

• 4/5

Calculating Slope from a table

Use the strategy called "First Differences" to determine the rise over the run.

Multiple Choice

What is the slope?

• -1/3

• -3

• -4

• 5

Calculate slope from two points

You can always calculate the slope by subtracting Y2-Y1 then dividing it by X2-X1. This problems are typically presented to you without a graph.

Multiple Choice

Find the slope of the line that passes through:

(-4, 7) and (-6, -4)

• 2/11

• 13/2

• 3/10

• 11/2

Multiple Choice

Find the slope of the line that passes through:

(-3, -4) and (7, 6)

• -1

• 0

• 1

• Undefined

Y-intercept

• The point where a line or curve crosses the y-axis of a graph

• In other words: it's the y-value when the x-value equals 0

• It is represented in y=mx+b as the b-value

Y-intercept calculated from a table

All you need to do is count backwards until the X-value (Guests) equals 0. The y-value paired with x=0 is the y-intercept.

Y-intercept calculated from two points

This can also be used to calculate the y-intercept if given a point and the slope.

Multiple Choice

Calculate the y-intercept of a line passing through (30, 440) with a slope of 8.

• (0, 240)

• (0, -240)

• (0, 200)

• (0, -200)

Multiple Choice

Calculate the y-intercept of the line that passes through (-4, 4) and (-10, -8)

• -12

• -4

• 4

• 12

Solving Linear Equations

• We always follow order of operations PEMDAS when solving

• One-variable linear equations can have one solution, infinite solutions or no solutions.

• The type of answer we get after solving tells us how many solutions there will be.

One Solution

Linear Equation

This has one solution because these two linear equations will only intersect at one coordinate point (-11, -37).

Infinite Solutions

Linear Equation

N=N means that all real numbers are solutions to this linear equation.

Notice there only appears to be one line on the graph. Make sure you know why!

No Solution

Linear Equation

• 0=14 tells us there are no solutions that will solve this linear equation.

• We could also determine that when the equation read 3x-6=3x+8

• The above essentially tells us these lines have equal slopes but different y-intercepts so they are parallel

Multiple Choice

How many solutions does this equation have? 3x + 2 = 4x + 6

• One Solution

• No Solution

• Infinite Solutions

Multiple Choice

How many solutions does this equation have? 3x -20 = 3x + 2

• No Solutions

• One Solution

• Infinite Solutions

Multiple Choice

How many solutions does this equation have?

 $3\left(x+1\right)-5=\frac{1}{2}\left(6x-4\right)$  

• No Solution

• One Solution

• Infinite Solutions

Inequalities

• Mathematics is not always about "equals", sometimes we only know that something is greater or less than

• An inequality tells us about the relative size of two values

• > greater than for example 

• < less than

• ≥ greater than or equal to

• ≤ less than or equal to

Inequalities on a Number Line

Remember the open and closed dot is no accident. They mean very specific things.

Multiple Choice

Which letter correctly represents the inequality in this image.

• A

• B

• C

• D

The Flippin' Inequality Rule

Flip the inequality sign when you multiply or divide both sides of an inequality by a negative number.

Multiple Choice

Solve:
6x+10>5x-12

• x>2
• x<2
• x<-22
• x>-22

Multiple Choice

You flip an inequality symbol when you...

• subtract
• multiply and divide only
• multiple by a negative number
• multiple or divide by a negative number

Multiple Choice

-2x + 3(-4x + 6) ≤116

• x ≤ -7

• x ≥ 29

• x ≥ -7

• x ≤ 29