Section 3.3 : Slope – Intercept Form

Learning Targets: F.IF.4 F.IF.7a, F.LE.2, and F.LE.5

Important Terms and Definitions

Linear Equation: An equation that models a linear function (straight line)

Linear Equations Non Linear Equations 2𝑥 + 3𝑦 = 1 2𝑥2 + 3𝑦 = 1 𝑦 = 1

4𝑥 𝑦2 = 1

4𝑥

𝑥 = 3 4𝑦 = 2𝑥3 + 8 𝑦 = 5 𝑥2 + 𝑦2 = 5

Linear Parent Function: The simplest form of a linear function. It is 𝑦 = 𝑥 or 𝑓(𝑥) = 𝑥

Slope – Intercept Form: 𝑦 = 𝑚𝑥 + 𝑏

Identifying Slope and y-intercept

In each of the following equations, identify the slope and the y-intercept.

Equation m b 𝑦 = 3𝑥 + 4

𝑦 =18 𝑥 − 1

𝑦 = −5𝑥 3𝑦 = −2𝑥 − 9 4𝑥 − 6𝑦 = 12

Writing an Equation Write an equation when given the slope and y-intercept.

Equation m b 1 −7 2

3 −9

−15 0

0 3 −2 1

4

y-intercept slope

Writing an Equation from a Graph

Write an equation in slope-intercept form for each graph.

(ex 11) (ex 12) (ex 13)

Writing an Equation from Two Points

Step One: Use 𝑚 = 𝑦2−𝑦1𝑥2−𝑥1

to find the slope.

Step Two: Use the slope and one of the given points, and plug in the 𝑥, 𝑦, and 𝑚 values to 𝑦 = 𝑚𝑥 + 𝑏. Then solve for b.

Step Three: Rewrite 𝑦 = 𝑚𝑥 + 𝑏 equation, substituting values for m and b

(ex 14) Write an equation in slope-intercept form for the line passing through the points (6, −4) and (−3, 5).

(ex 15) Write an equation in slope-intercept form for the line passing through the points (−1, −5) and (−7, −6).

Graphing a Function in Slope-Intercept Form

Step One: Plot the y-intercept

Step Two: Use the slope to get from the y-intercept to the next point

Find the slope and y-intercept of each line. Then graph the line.

(ex 16) 𝑦 = 3𝑥 − 5 (ex 17) 6𝑥 + 3𝑦 = 12

(ex 18) −2(3𝑥 − 4) + 𝑦 = 0 (ex 19) 4𝑥 + 3𝑦 = 2𝑥 − 1

(ex 20) A dance instructor charges a $45 fee for a ballet lessons, plus $25 per hour. Write an equation to model the cost y of a lesson that takes x hours. Then graph the function.

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Investigating Slope Name_________________________________ (using the graphing calculator)

1. Graph these lines which have positive slope. Sketch the graphs on the grid at the right.

What do you notice about lines with positive slopes? What happens to the lines as these positive slopes increase (get bigger)?

2. Graph these lines that have negative slopes.

What do you notice about lines with negative slopes?

What happens to the lines as these negative slopes decrease (get smaller)?

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3. Graph these lines that have zero slopes.

What do you notice about lines with a zero slope?

How are all of these lines related to one another?

4. Graph these lines that have the same slopes.

What do you notice about lines with the same slope?

State a rule based on your observations about lines having the same slopes.

Homework – Section 3.3 : Slope-Intercept Form

Identify the slope and y-intercept in each equation. Then graph the line. (Note – don’t graph #6)

1. 𝑦 = 𝑥 + 2 4. 2𝑦 − 6 = 3𝑥 2. 𝑦 = − 1

3𝑥 + 1

2 5. −2𝑦 = 6(5 − 3𝑥)

3. 4𝑦 = 8𝑥 − 3 6. 𝑦 = (2 − 𝑎)𝑥 + 𝑎

Write an equation when given the slope and y-intercept.

7. 𝑚 = 12, 𝑏 = −8 10. 𝑚 = 0, 𝑏 = 1

8. 𝑚 = 5, 𝑏 = 2 11. 𝑚 = 195, 𝑏 = 0

9. 𝑚 = −43, 𝑏 = −5

2 12. 𝑚 = −2

7, 𝑏 = 9

17

Write an equation in slope-intercept form for each graph.

13. 14. 15.

Write an equation in slope-intercept form that passes through the two given points.

16. (−2, 6) and (5, 1) 17. (2, 7) and (1,−4) 18. (1

2, 2) and (− 3

2, 4)

19. iTunes is currently offering a promo code to get three dollars off your total purchase. The current cost per song is $1.25. Write an equation that models the total cost, c, based on the number of songs your purchase, s, and the discount. Then graph the equation. What is the cost of 12 songs?

20. A candle begins burning at time 𝑡 = 0. Its original height is 14 inches, and after 30 minutes, the height is 10 inches. Write an equation that relates the height of the candle to the time it has been burning. How many minutes after the candle is lit will it burn out?