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STATION #1: Writing Equations in FUNCTION FORM β¦in other words, get y all by itself on one side of the equal sign!!! Example: Write 9π₯ β 4π¦ = 8 in function form 9π₯ β 4π¦ = 8 Write original equation 9π₯ β 4π¦ = 8 β9π₯ β9π₯ First isolate the term containing π¦ β4π¦ = 8 β 9π₯ Subtract 9π₯ from both sides β4π¦ = 8 β 9π₯ Now get π¦ all by itself β4 β4 β4 9 π¦ = β2 + π₯ 4 Divide both sides by β4 9 The equation π¦ = β2 + π₯ is in function form!! 4 STATION #2: Graphing using a TABLE OF VALUES Example: Graph the equation 3π¦ = 6π₯ β 3. STEP 1: Solve the equation for y 3π¦ = 6π₯ β 3 π¦ = 2π₯ β 1 STEP 2: x -2 -1 0 1 2 (divide both sides by 3) Make a table of values by choosing 5 values for x (2 positive, 2 negative, and zero). Find the values of y for each of these x-values. y Example for π₯ = β2 π¦ = 2(β2) β 1 π¦ = β4 β 1 π¦ = β5 x -2 -1 0 1 2 y -5 -3 -1 1 3 STEP 3: Plot the points. Notice that the points appear to lie on a line. STEP 4: Connect the points by drawing a line through them. Use arrows to indicate that the graph goes on without end. 2 2 STATION #3: Graphing using INTERCEPTS Example: Graph 2π₯ β 4π¦ = 16 using intercepts. STEP 1: Find the x-intercept: Substitute y = 0 and solve for x 2π₯ β 4(0) = 16 2π₯ = 16 π₯=8 STEP 2: The graph crosses the x-axis at (8, 0). Find the y-intercept: Substitute x = 0 and solve for y 2(0) β 4π¦ = 16 β4π¦ = 16 π¦ = β4 The graph crosses the y-axis at (0, β4). STEP 3: Plot & Label the two ordered pairs from Step 1 and Step 2 STEP 4: Connect the points by drawing a line through them. Use arrows to indicate that the graph goes on without end. 2 2 (0, -4) (8, 0) STATION #4: HORIZONTAL & VERTICAL LINES Horizontal Lines: Equations of horizontal lines only have a y-variable Example: y = -5 Remember: The equal sign (=), represents the word βisβ in a sentence. (0, -5) So the equation y = -5 can be thought of as βeverywhere y is -5β Consider the table of values for y = -5: x 4 -2 3 -9 10 y -5 -5 -5 -5 -5 y is always -5!! It doesnβt matter what value you choose for x Vertical Lines: Equations of horizontal lines only have a x-variable Example: x = 4 The equation x = 4 can be thought of as βeverywhere x is 4β (4, 0) Consider the table of values for x = 4: x 4 4 4 4 4 y -5 2 -12 34 5 x is always 4!! It doesnβt matter what value you choose for y!! STATION #5: Finding SLOPE Example 1: Recall: The slope of a line rising from left to right will be positive. The slope of a line falling from left to right will be negative. Example 2: Recall: The slope of all horizontal lines will be zero. The slope of all vertical lines will be undefined. STATION #6: Graph using SLOPE-INTERCEPT FORM Example: STATION #7: REVIEW Example 1: Example 2: