Bell Ringer Rewrite 5x + y = 8 so that y is a function of x. (solve for y) Find the slope of a line going through (-5, 6) and (0, 8) Find the x and y intercepts.

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Presentation transcript:

Bell Ringer Rewrite 5x + y = 8 so that y is a function of x. (solve for y) Find the slope of a line going through (-5, 6) and (0, 8) Find the x and y intercepts of y = 20x - 600

4.5 Graph Using Slope-Intercept Form

Starting at a Point, Finding the Next If I start at (0, 1) and have a slope of 2/3 where is my next point What if my slope is -2/3? If I start at (0, -4) and have a slope of ½ where is my next point?

Slope Intercept Form y = mx + b m = slope b = y-intercept (0, b) Trick to remember m = mountain = slope b = beginning (where we begin our graph)

Find the Slope and y-intercept y = 3x + 4 y = ½x - 2 3x + y = 2 x + 3y = 9

Guided Practice 1 – 3 on Page 244

Using Slope-Intercept Form to Graph Graph each 1. y = ½x y = 3x y = 5x – x + y = x – 3y = x + 4y = 6 7. x + 3y = 9

ESCALATORS EXAMPLE 3 Change slopes of lines To get from one floor to another at a library, you can take either the stairs or the escalator. You can climb stairs at a rate of 1.75 feet per second, and the escalator rises at a rate of 2 feet per second. You have to travel a vertical distance of 28 feet. The equations model the vertical distance d (in feet) you have left to travel after t seconds. Stairs: d = –1.75t + 28 Escalator: d = –2t + 28

EXAMPLE 3 Change slopes of lines a. Graph the equations in the same coordinate plane. b. How much time do you save by taking the escalator ? SOLUTION a. Draw the graph of d = –1.75t + 28 using the fact that the d- intercept is 28 and the slope is –1.75. Similarly, draw the graph of d = –2t The graphs make sense only in the first quadrant.

EXAMPLE 3 Change slopes of lines The equation d = –1.75t + 28 has a t- intercept of 16. The equation d = –2t + 28 has a t- intercept of 14. So, you save 16 – 14 = 2 seconds by taking the escalator. b.

EXAMPLE 4 Change intercepts of lines TELEVISION A company produced two 30 second commercials, one for $300,000 and the second for $400,000. Each airing of either commercial on a particular station costs $150,000. The cost C ( in thousands of dollars ) to produce the first commercial and air it n times is given by C = 150n The cost to produce the second and air it n times is given by C = 150n a. Graph both equations in the same coordinate plane.

EXAMPLE 4 Change intercepts of lines b. Based on the graphs, what is the difference of the costs to produce each commercial and air it 2 times? 4 times? What do you notice about the differences of the costs? SOLUTION a. The graphs of the equations are shown.

EXAMPLE 4 Change intercepts of lines b. You can see that the vertical distance between the lines is $100,000 when n = 2 and n = 4. The difference of the costs is $100,000 no matter how many times the commercials are aired.

Parallel Lines and Slope What do you know about parallel lines? What would you expect about the slopes of parallel lines? Example 5

Homework 2 – 16 even, 17 – 20, 22 – 44 even Quiz tomorrow over 4.4 – 4.5