slope and y intercept
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- 1. March 24, 2011SLOPE AND Y-INTERCEPT
2. What is slope? The slope of a line is the ratio that describesits tilt. The slope of a line can be:Positive Negative 3. What is slope?Zero Undefined 4. How do we find the slope?1. Find two points on the line with coordinates that are easy to read. 5. How do we find the slope?2. Between these two points, find the rise (the change in y going up or down) and the run(the change in x going left or right) .Rise=3 Run= 4 6. How do we find the slope?3. To find the slope, divide the rise by the run. Rise=3Run= 4 7. STOPNow, work problems 1 and 2 on the Reteaching 8-3 worksheet.Answer to #1: -3Answer to #2: -5/2 8. Another way to find the slope We can also find the slope using only thecoordinates of the two points. Suppose we have points A (4,5) and B (0,2). To find the slope, find the difference betweenthe y-coordinates of A and B (the rise) anddivide it by the difference between the x-coordinates (the run). 9. STOPNow, work problems 3 and 6 on the Reteaching 8-3 worksheet.Answer to #3: 1/4Answer to #6: 3 10. Finding the equation of a line Now that we know the slope of our line, wecan find its equation using slope-interceptform. But before we can do this, we must find the y-intercept of the line. Y-intercept= the value of y when x is zero 11. Finding the equation of a line To find the y-intercept, follow the y-axisupward or downward until you reach the line.Y-intercept=2 12. Finding the equation of a line Now that we know the slope and y-intercept,we use this equation: y = mx + bwhere m is the slope and b is the y-intercept.Since our slope was m=3/4 and our y-interceptwas b=2, the equation of our line is: y= x + 2. 13. STOPNow, work problem #1 on the Practice 8-4 worksheet.Answer to #1: y = -5/4 x + 2 14. Graphing Linear EquationsNow that we know y= mx + b, we can graphlinear equations much more easily.Lets try the equation: y= 2/3 x + 11. Identify m(slope) and b(y-intercept). In this case, m= 2/3 and b= 1. 15. Graphing Linear Equations2. Place a point at (0, b). An easy way toremember this is that b is for begin. In thiscase, that would be the point (0,1). 16. Graphing Linear Equations3. Now, use the slope to plot another point. We know that our slope is 2/3, so we want to go up 2 units and 3 units to the right. 17. Graphing Linear Equations4. Next, connect the two points with a ruler or straightedge, extending the line in both directions. 18. STOPWork problem 9 on the Practice 8-3 worksheet.Answer to #9: 19. Writing a Linear Equation from a Table Suppose you are given a table like this: x y-2-11 0 -5 21 47 20. Writing a Linear Equation from a Table1. First, look for a pattern on each side of the table. For this table, we notice:xy -2-11 +6+20 -5+2 +621+2 +647 21. Writing a Linear Equation from a Table2. Next, divide the change in y by the change in x to get the slope. In this case,3. To find the y-intercept, we simply look at the table and find the value of y when x=0. In this case, y= -5. 22. Writing a Linear Equation from a Table4. Now that we have m=3 and b= -5, we canplug these values into y= mx + b to get ourequation.So we have y= 3x 5. 23. STOPNow, work problems 1 and 2 from the Reteaching 8-4 worksheet.Answer to #1: y= 7xAnswer to #2: y= x - 8 24. THE ENDHave a wonderful day!