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TEST REVIEW GRADE 8 MATHSLOPE OR RATE OF CHANGE4 DIFFERENT TYPES OF SLOPESThe slope of a line (Also called Rate of Change)The slope of a line is a number that measures the “steepness" of the line. Slope is usually denoted by the letter m. It is the ratio of the change in y (rise or y2 – y1) divided by the change in x (run or x2 – x1).WRITING AN EQUATION IN SLOPE-INTERCEPT FORMFrom a Tablex-10123y108642STEP 1- Choose any two ordered pairs (x1, y1) and (x2, y2) from the tableSTEP 2- Use slope formula to find the slopeSTEP 3 – Find the y-interceptSTEP 4- Use the slope and the y-intercept to write the equation in slope-intercept form (y = mx + b) Example (Using the Table Above) Choose (1, 6) and (3, 2) from the tableX1 = 1 X2 = 3 Y1= 6 Y2=2m = 2 - 6 = -4 = -2 3 – 1 2Determine the y-interceptY-Intercept from table (0, 8)Use the slope and y-intercept to write the equation in slope-intercept form (y = mx + b) y = -2x + 8 WRITING AN EQUATION IN SLOPE-INTERCEPT FORMFrom a Graph STEP 1- Find the slope or rate of changeChoose any two points that fall on the line (0, 1) and (2,4) Use the graph to find the rise ÷ run = 32 OR Use slope formula to find the slope (0, 1) and (2,4)m = 4 – 1 = 3 2 – 0 2 67564031115STEP 2 – Identify the y-intercept (0, 1) and write the equation y = (3/2)x + 1 or y = 1.5x + 1 TEST REVIEW GRADE 8 MATHREAL WORLD APPLICATION- EXPLAIN THE MEANING OF THE SLOPE AND Y-INTERCEPTReal world context (Find the slope or the account balance per month) STEP 1- CHOOSE TWO ORDERED PAIRS Choose any two points that fall on the line Example: (0, 300) and (2,500)STEP 2- FIND THE SLOPEUse the slope formula or make a right triangle and divide the rise by the run (m = 100)STEP 3- WRITE THE EQUATIONWrite the equation in slope-intercept form using the slope of 100 and the y-intercept from the graph of (0, 300) : y = 100x + 300MEANING OF SLOPE (m = 100)Explain the ratio of the rise (100) to the run (1).The number of dollars in John’s savings account increases by $100 each month.MEANING OF Y-INTERCEPT (b = 300)John started out with $300 in his saving account (Y-INTERCEPT = INITIAL VALUE)TEST REVIEW GRADE 8 MATHWRITE AN EQUATION IN STANDARD FORMWrite the equation y = ? x + 9 in standard form (Ax + By = C)STEP 1-Multiply by the LCD (of 2) to eliminate fractions2y = 2(1/2 x) + 2(9)2y = x + 18STEP 2- Change to standard form(subtract x from both sides)-x + 2y = 18WRITING THE EQUATION OF A LINE WHEN GIVEN TWO ORDERED PAIRS (IN A TABLE, ON A GRAPH, OR OUTSIDE A TABLE)------EXAMPLE (2, 6) AND (4, 10)STEP 1- Find the slope Use slope formula to find the slopeExample: Find the slope of a line passing through (2, 6) and (4, 10) Slope = (10 – 6) ÷ (4 – 2) Slope = 2STEP 2- Find the Y-InterceptSubstitute slope (m = 2) and one of the two ordered pairs (4, 10) in y= mx + b then solve for by = mx + b10 = 2(4) + b10 = 6 + bb = 4STEP 3- Write the equation using the slope and y-intercepty = 2x + 4 ................
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