Unit 4 Review! Objective: to review linear equations Common Core State Standards 8.EE.5; 8.EE.6; 8.EE.7; 8.EE.8

4 Properties of Equality 1)If A = B, Then A + C = B + C If 5 = 5, Then = ) If A = B, Then A – C = B – C If 5 = 5, Then = 5 – 3 3) If A = B, Then A * C = B * C If 5 = 5, Then 5 * 3 = 5 * 3 4) If A = B, Then A/C =B/C, Where C ≠ 0 If 5 = 5, Then 5 / 3 = 5 / 3

Rules for Equations 1)GOAL: Isolate the variable on one side of the equation. 2) Always perform the same operation to both sides of an equation to keep it balanced. 3) To undo an operation, perform its opposite operation to both sides of the equation. (INVERSE OPERATIONS SADMEP) 4) Check your work by plugging in your answer back into original equation to see if both sides are balanced

Inverse Operations Operation PEMDASInverse Operation SADMEP AdditionSubtraction Addition MultiplicationDivision Multiplication FractionMultiplicative Inverse (flip fraction)

Writing Equations 1) Explore the Problem: To solve a verbal problem, first read the problem carefully and explore what the problem is about. Identify what information is given (KEY WORDS). Identify what you are asked to find. 2) Plan the Solution: One strategy you can use to solve a problem is to write an equation. Choose a variable to represent one of the unspecific numbers in the problem (defining a variable). Use the variable to write expressions for the other unspecified numbers in the problem 3) Solve: Use your strategy to solve the problem. If your plan does not work, revise it or make a new plan. 4) Examine: Check your answer in the context of the original problem. Does your answer make sense? If not, solve the problem another way.

Key Words Translation increased by; more than; combined; together; total of; sum; plus; added to Addition decreased by; minus; less than; difference; fewer than Subtraction of; times; product of; increased/decreased by a factor of Multiplication per; a; out of; ratio of; quotient; percent Division is; are; was; were; gives; yieldsEquals

Variables & Constants on Both Sides 1)Simplify each side separately (if possible) by combining like terms. 2) Perform inverse operations to put variables on one side of the equal sign and the constants on the other side of the equal sign. 3) Solve for the variable 4) Check your work by plugging in your answer back into original equation to see if both sides are balanced

Special Cases 1) An equation has no solution if no value of the variable makes the equation true. Ex: 2x=2x+1 or 7 = 6 2) An equation that is true for every value of the variable is an identity (infinite solutions). Ex: 2x=2x or 2 = 2 or 0 = 0

Constant Rate of Change constant rate of change: the rate of change between any two points in a linear relationship is the same or constant (difference in Y’s divided by difference in X’s). The line formed will be a linear graph (a straight line graph). The first column is your X values, the second column is your Y values. The first row is your X values, the second row is your Y values.

Constant Rate of Change The Y’s are increasing by 8, the X’s are increasing by 1. Rate of change is 8/1 The Y’s are increasing by 9, the X’s are increasing by 5. Rate of change is 9/5

Slope You can also find the slope by putting your points in a table and finding the constant rate of change! Types of Slope

Slope-Intercept Form slope-intercept form: An equation written in the form y = mx + b, where m is the slope and b is the y-intercept. X & Y Intercepts The x-intercept is where the graph crosses the x-axis. The y-coordinate is always 0. The y-intercept is where the graph crosses the y-axis. The x-coordinate is always 0.

x-intercept: Plug in 0 for y. -3x - 5(0) = 9 -3x = 9 x = -3; (-3, 0) y-intercept: Plug in 0 for x. -3(0) + 5y = 9 5y = 9 y = ; (0, ) Example: Find the x- and y-intercepts. -3x + 5y = 9

Remember the word “ VUXHOY ” Vertical lines Undefined slope X = number; This is the equation of the line (ex: x=4) Horizontal lines O - zero is the slope Y = number; This is the equation of the line (ex: y=-3)

Point Slope Formula If you know two points on a line, first use them to find the slope. Then you can write an equation using either point. 1)Find the slope of the line with the given points 2)Use either point and the slope to plug into the equation: y – y1 = m(x-x1) Where m = slope, x1 = x coordinate and y1 = y coordinate

Systems of Equations A system of equations is when you have two or more equations using the same variables. The solution to the system satisfies ALL of the equations. y x y x Lines intersect one solution Lines are parallel no solution y x Lines coincide infinitely many solutions There are 3 steps to solving a system using a graph. Step 1: Graph both equations: Graph using slope and y – intercept or x- and y-intercepts. Be sure to use a ruler and graph paper! Step 2: Do the graphs intersect?:This is the solution! LABEL the solution! (x, y) form Step 3: Check your solution: Substitute the x and y values into both equations to verify the point is a solution to both equations

Step 1: Solve an equation for one variable. Step 2: Substitute Step 3: Solve the equation. Step 4: Plug back in to find the other variable. Step 5: Check your solution. Pick the easier equation. The goal is to get y= ; x= ; a= ; etc. Put the equation solved in Step 1 into the other equation. Get the variable by itself. Substitute the value of the variable into the equation. Substitute your ordered pair into BOTH equations. Systems of Equations with Algebra

Example: Solve the system with Algebra x + y = 5 y = 3 + x Step 1: Solve an equation for one variable. Step 2: Substitute The second equation is already solved for y! x + y = 5 x + (3 + x) = 5 Step 3: Solve the equation. 2x + 3 = 5 2x = 2 x = 1 Step 4: Plug back in to find the other variable. Step 5: Check your solution. (1) + y = 5 y = 4 (1) + (4) = 5 (4) = 3 + (1)

Let’s Practice! MAP PLUS BOOKLET QUESTIONS #2, 19, 22, 23, 25, 28, 30, 31, 33, 40, 48, 49, 58, 59, 62, 67, 68, 69, 75, After reviewing and practicing Unit 4, rate yourself on how you feel about the same questions in the MAP Plus Book. Exit Ticket