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Slope & y-intercept on the Coordinate Plane

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## Slope & y-intercept on the Coordinate Plane

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**Slope & y-intercept**on the Coordinate Plane Return to Table of Contents Day 2**Consider this graph of the Cartesian Plane, also called a**Coordinate Plane or XY-Plane. Imagine trying to tell a person how to draw a line on the Cartesian Plane.**The Equation of a Line**y You only need a few facts about a line to completely describe it: ·Its y-intercept (where it crosses the y-axis) "b" · Its slope (how much it rises or falls) "m" · y = mx + b 10 8 6 4 2 x 0 -8 -4 -2 -10 -6 2 4 6 10 8 -2 -4 -6 -8 -10**The y-intercept**y The y-intercept ("b")of a line is the point where the line intercepts the y-axis. In this case, the y-intercept of the line is +4. 10 8 6 4 This is the ordered pair (0,4). 2 x 0 -8 -4 -2 -10 -6 2 4 6 10 8 -2 -4 -6 -8 -10**11**What is the y-intercept of this line? b = 6 Answer (click me)**12**What is the y-intercept of this line? b = -4 Answer (click me)**13**What is the y-intercept of this line? b = 8 Answer (click me)**y**14 What is the x-intercept of this line? 10 8 6 4 2 x 0 -8 -4 -2 -10 -6 2 4 6 10 8 -2 -4 (-4,0) -6 Answer (click me) -8 -10**15**What is the x-intercept of this line? (3,0) Answer (click me)**16**What is the x-intercept of this line? (-6,0) Answer (click me)**17**The graph of the equation x + 3y = 6 intersects the y-axis at the point whose coordinates are A (0,2) B (0,6) C (0,18) D (6,0) From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.**Defining Slope on the Coordinate Plane**Return to Table of Contents**Consider this...**y An infinite number of lines can pass through the same location on the y-axis...they all have the same y-intercept. Examples of lines with a y-intercept of ____ are shown on this graph. What's the difference between them (other than their color)? 10 8 6 4 2 x 0 -8 -4 -2 -10 -6 2 4 6 10 8 -2 -4 -6 -8 -10**The Slope of a Line**y The lines all have a different slope. Slope is the steepness of a line. Compare the steepness of the lines on the right. Slope can also be thought of as the rate of change. 10 8 6 4 2 x 0 -8 -4 -2 -10 -6 2 4 6 10 8 -2 -4 -6 -8 -10**The Slope of a Line**run y The red line has a positive slope, since the line rises from left to the right. 10 rise 8 6 4 2 x 0 -8 -4 -2 -10 -6 2 4 6 10 8 -2 -4 -6 -8 -10**The Slope of a Line**y The orange line has a negative slope, since the line falls down from left to the right. 10 8 6 rise 4 run 2 x 0 -8 -4 -2 -10 -6 2 4 6 10 8 -2 -4 -6 -8 -10**The Slope of a Line**y 10 The purple line has a slope of zero, since it doesn't rise at all as you go from left to right on the x-axis. 8 6 4 2 x 0 -2 -8 -4 -10 -6 2 4 6 10 8 -2 -4 -6 -8 -10**The Slope of a Line**The black line is a vertical line. It has an undefined slope, since it doesn't run at all as you go from the bottom to the top on the y-axis. rise 0 = undefined**18**Is the slope of the following graph positive, negative, zero, or undefined? A positive B negative C zero D undefined**19**Is the slope of the following graph positive, negative, zero, or undefined? A positive B negative C zero D undefined**20**Is the slope of the following graph positive, negative, zero, or undefined? A positive B negative C zero D undefined**21**Is the slope of the following graph positive, negative, zero, or undefined? A positive B negative C zero D undefined**22**Is the slope of the following graph positive, negative, zero,or undefined A positive B negative C zero D undefined**Is the slope of the following graph positive, negative,**zero, or undefined? 23 A positive B negative C zero D undefined**24**Is the slope of the following graph positive, negative, zero, or undefined? A positive B negative C zero D undefined**25**Is the slope of the following graph positive, negative, zero, or undefined? A positive B negative C zero D undefined**Measuring the Slope of a Line**While we can quickly see if the slope of a line is positive, negative or zero...we also need to determine how much slope it has...we have to measure the slope of a line.**Measuring the Slope of a Line**The slope of the line is just the ratio of its rise over its run. The symbol for slope is "m". So the formula for slope is: rise slope = run**Measuring the Slope of a Line**rise slope = run The slope is the same anywhere on a line, so it can be measured anywhere on the line. Keep in mind the direction: · Up (+) Down (-) · Right (+) Left (-)**Measuring the Slope of a Line**For instance, in this case we measure the slope by using a run from x = 0 to x = +6: a run of 6. During that run, the line rises from y = 0 to y = 8: a rise of 8. rise 8 slope = m = run 6 4 m = 3**Measuring the Slope of a Line**But we get the same result with a run from x = 0 to x = +3: a run of 3. During that run, the line rises from y = 0 to y = 4: a rise of 4. rise 4 m = slope = 3 run**Measuring the Slope of a Line**But we can also start at x = 3 and run to x = 6 : a run of 3. During that run, the line rises from y = 3 to y = 7: a rise of 4. 4 m = 3 rise slope = run**Measuring the Slope of a Line**But we can also start at x = -6 and run to x = 0: a run of 6. During that run, the line rises from y = -8 to y = 0: a rise of 8. 8 m = 6 rise slope = 4 run m = 3**Measuring the Slope of a Line**How is the slope different on this coordinate plane? The line rises 8, however the run goes left 6 (negative). Therefore, it is said to have a negative slope rise slope = run 8 m = -6 -4 m = 3 *most often the negative sign is placed in the numerator**26**What's the slope of this line?**27**What's the slope of this line?**28**What's the slope of this line?**29**What's the slope of this line?**30**What's the slope of this line?**31**What's the slope of this line? A -20 B 0 C 20 D undefined**32**In the diagram below, what is the slope of the line passing through points A and B? A -2 B . B 2 A C -1/2 D 1/2 From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011**33**A straight line with slope 5 contains the points (1,2) and (3,K). Find the value of K. [The use of the accompanying grid is optional.] From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.**Tables and Slope**Return to Table of Contents**How can slope and the y-intercept be found within the table?**· Look for the change in the y-values · Look for the change in the x-values · Write as a ratio (simpified) - this will be the "slope" · Determine the corresponding y-value to the x-value of 0 - this will be the "y-intercept"**+3**+6 +3 +6 5 is the y-intercept 6 3 2 is the slope =**Determine the slope and y-intercept from this table.**is the slope -4 is the y-intercept click to reveal answer**34**What is the slope?**35**What is the y-intercept? You may have to do a little extra work for this one...**36**What is the slope?