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☺ A technique in which a straight line is fitted to a set of data points to measure the effect of a single independent variable. The slope of the line is the measured impact of that variable. Sample Make a scatter plot for these set of points. Sketch a line which best fits this set of data and find its equation. Points scored in ten games. Minutes Points played scored 28 16 35 13 8 2 20 12 39 31 23 10 19 9 27 15 15 4 30 19 Answer: Points scored p= 0.75m-5 40 30 20 10 0 10 20 30 40 Time (min) To guess based on observations . There are 4 blue M&M’s, 5 yellow, 3 brown, and 2 green in a jar. If Carmen eats 1 green M&M and 2 yellow M&M’s, what is the prediction of the next M&M being yellow ? Answer: 3/11 REMEMBER: o Total number of M&M’s=14 o 4 blue o 5 yellow o 3 brown o 2 green o She ate 1 green and 2 yellow M&M’s 14 M&M’s minus 3 M&M’s equals to 11 M&M’s left in the jar. 5 yellow M&M’s minus 2 yellow M&M’s equal to 3 yellow M&M’s left that can possibly be taken out. Number of yellow M&M’s left in jar Total Number of M&M’s left in jar Answer:3/11 Like in math, the prediction of 2012 is being predicted by the information given off from the Mayan calendar. Two variables x and y show direct variation provided that y= ax where a is a nonzero constant. Given: y varies directly as x, and y=14 when x=3.5. Write and graph the direct variation function. 8 6 4 2 -8 -6 -4 -2-2 -4 -6 -8 2 4 6 8 y= kx y varies directly as x. 14= k(3.5) substitute 14 for y and 3.5 for x. 4=k solve for the constant of variation k. Y= 4x Write the variation function by using the value of k. Graph the direct variation function. The y-intercept is 0, and the slope is 4. Check substitute the original values of x and y into the equation. Y=4x 14 4(3.5) 14 14 Y=2x+5 Continually occurring or recurring Like in a graph where a constant line goes up or down constantly, the man in this picture is constantly going up the stairs like shown to your left. The nonzero constant a in a direct variation equation y=ax. In a constant Variation, like the graph shown to your left, as x increases y increases and as x decreases y decreases. 9 6 3 -9 -6 -3 3 -3 -6 -9 6 9 Note: this can also be written as k=y/x The x coordinate of a point where a graph intercepts the x-axis Y-intercept…(-1,0) X-intercept…(0,1) The y coordinate of a point where a graph intercepts the y-axis Y-intercept X-intercept Related by direct variation A pizza that is directly proportionally cut into four slices is a life example of how a line is directly proportional on a graph. Hope you had fun with us on Objective 3!! Good luck on TAKS and remember… Practice makes Perfect.”