Tables and Slope Return to Table of Contents. xy -3 05 311 How can slope and the y-intercept be found within the table? · Look for the change in the y-values.

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Presentation transcript:

Tables and Slope Return to Table of Contents

xy 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"

xy = 2 is the slope 5 is the y-intercept

-4 is the y-intercept is the slope xy Determine the slope and y-intercept from this table. click to reveal answer

34 xy What is the slope?

35 xy What is the y-intercept? You may have to do a little extra work for this one...

36 xy What is the slope?

37 xy What is the y-intercept? You may have to do a little extra work for this one...

38 xy What is the slope?

Another Application of the Definition of Slope Slope of a line is meant to measure how fast it is climbing or descending. A road might rise 1 foot for every 10 feet of horizontal distance. 10 feet 1 foot The ratio, 1/10, which is called slope, is a measure of the steepness of the hill. Engineers call this use of slope grade. What do you think a grade of 4% means?

Slope of 3/20 20 feet 3 feet 7 feet slope of -3/7 (The grade of this hill is 3/20 =.15= 15%) (The grade of this hill is 3/7 =.43= 43%)

y = mx + b Return to Table of Contents Slope-Intercept Form

Once you have identified the slope and y-intercept in an equation, it is easy to graph it! To graph y = 3x follow these steps: · Plot the y-intercept, in this case (0, 5) · Use the simplified rise over run to plot the next point - in this case, from (0, 5) go UP 3 units and RIGHT 1 unit to plot the next point. Connect the points.

Try this...graph y = -2x - 3 · Start at the y-intercept - plot it. · From the y-intercept, use the slope "m" to plot the next point. How would you use rise over run to plot -2? · Connect the points. Did you have different points plotted? Does it make a difference?

Try this...graph 4y = x + 12 (is this in y=mx + b form?) · Start at the y-intercept - plot it. · From the y-intercept, use the slope "m" to plot the next point. How would you use rise over run to plot it? · Connect the points. Did you have different points plotted? Does it make a difference?

Try this...graph 5x + y = - 4 (is this in y=mx + b form?) · Start at the y-intercept - plot it. · From the y-intercept, use the slope "m" to plot the next point. How would you use rise over run to plot it? · Connect the points. Did you have different points plotted? Does it make a difference?

Position of a Line

What are the similarities and differences between the lines below?

The lines were in the form of y = mx+b.

So it is the b in y = mx + b that is responsible for the position of the line.

What determines slope? Examine the following equations: y = 2x + 1 y = 3x + 1 y = -1/2 x + 1 y = -x + 1 What do the equations have in common? What is different?

Any equation of the form y = mx + b gives a line where b is the y intercept m is the slope

44Which equation does the graph represent? Ay = -6x-6 By = -1x+6 Cy = 6x+6 Dy = x-6 y x

45Which equation does the graph represent? Ay = 4x By = x+4 Cy = 4 Dy = x y x

46Which equation does the graph represent? A B C D y x

47Which equation does the graph represent? A B C D y x

48Which equation does the graph represent? Ay = 10x+10 By = -2x+10 Cy = 5x+10 Dy = -5x+10 y x

49Which graph represents the equation y = 3x-2? Aline A Bline B Cline C Dline D y x A B C D

51Which graph represents Aline A Bline B Cline C Dline D y x A B C D