Lesson 3 4 Equations of Lines Transparency 3

Lesson 3 -4 Equations of Lines

Transparency 3 -4 5 -Minute Check on Lesson 3 -3 Find the slope of each line for M(– 3, 4) and N(5, – 8). 1. MN 2. a line perpendicular to MN – 3/2 2/3 3. a line parallel to MN – 3/2 Graph the line that satisfies each condition. 4. slope = 4 and contains (1, 2) 6. Standardized Test Practice: 5. slope = 0 and contains (– 3, – 4) Use slope to find a relationship between CD and EF for C(4, 5), D(– 1, 15), E(– 4, – 6), F(0, – 8). A CD || EF B CD EF C neither || nor D not enough information given

Objectives • Write an equation of a line given information about its graph • Solve problems by writing equations

Vocabulary: Equations of Lines • Slope – Intercept Form: y = mx + b • Point Slope Form: y – y 1 = m(x – x 1) • From two points: (y 2 – y 1) y – yp = –––– (x – xp) (x 2 – x 1) m is the slope b is the y-intercept m is the slope (x 1, y 1) is the given point (y 2 – y 1) / (x 2 – x 1) is the slope p is one of the given points

Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of – 3. Slope-intercept form Answer: The slope-intercept form of the equation of the line is

Write an equation in point-slope form of the line whose slope is that contains (– 10, 8). Point-slope form Simplify. Answer:

Write an equation in point-slope form of the line whose slope is Answer: that contains (6, – 3).

Write an equation in slope-intercept form for a line containing (4, 9) and (– 2, 0). Find the slope of the line. Slope formula Simplify.

Now use the point-slope form and either point to write an equation. Using (4, 9): Point-slope form Distributive Property Add 9 to each side.

Using (– 2, 0): Point-slope form Simplify. Distributive Property Answer:

Write an equation in slope-intercept form for a line containing (3, 2) and (6, 8). Answer:

Write an equation in slope-intercept form for a line containing (1, 7) that is perpendicular to the line the slope of a line perpendicular to it is 2. Point-slope form Distributive Property Add 7 to each side.

Write an equation in slope-intercept form for a line containing (– 3, 4) that is perpendicular to the line Answer:

RENTAL COSTS An apartment complex charges $525 per month plus a $750 security deposit. Write an equation to represent the total annual cost A for r months of rent. For each month of rent, the cost increases by $525. So the rate of change, or slope, is 525. The y-intercept is located where 0 months are rented, or $750. Slope-intercept form Answer: The total annual cost can be represented by the equation

RENTAL COSTS An apartment complex charges $525 per month plus a $750 security deposit. Compare this rental cost to a complex which charges a $200 security deposit but $600 per month for rent. If a person expects to stay in an apartment for one year, which complex offers the better rate? First complex: Second complex: Simplify. Answer: The first complex offers the better rate: one year costs $7050 instead of $7400.

RENTAL COSTS A car rental company charges $25 per day plus a $100 deposit. a. Write an equation to represent the total cost C for d days of use. Answer: b. Compare this rental cost to a company which charges a $50 deposit but $35 per day for use. If a person expects to rent a car for 9 days, which company offers the better rate? Answer: The first company offers the better rate. Nine days cost $325 instead of $365.

Summary & Homework • Summary: – An equation of a line can be written if you are given: • The slope and the y intercept, or • The slope and the coordinates of a point on the line, or • The coordinates of two points on the line • Homework: pg 148 -149: 15 -19, 21, 35, 37, 47