Unit 2Analytic Geometry

Introduction: Review of Key Concepts

Learning Goal: I can solve problems involving slopes, equations of lines and Pythagorean

theorem

Warm-Up: Fractions1) Place the following fractions in order from smallest

to largest: ¼, ⅓, ⅖, ⅞, ¾, ⅔, 2⅗

2) Complete the following operations with fractionsa) ½ + ⅓ b) ¼ × ⅚ c) ⅙ ÷ ⅜

d) ⅝ - ⅖

Equations of Lines

• y = mx +b form (ex. y = 3x – 7)– Isolate y y = mx + b

m = slope b= y-

intercept

• Standard Form (ex. 4x – 3y = -1)– ax + by = c, where a is positive and a, b, and c are

whole numbers (no fractions or decimals)

Rearranging EquationsPut the following equations in: a) y = mx + b form

i) 4x + 2y = 8 ii) ⅓x = -⅔y - 4

b) standard formi) -9x + 4y - 6 = 0 ii) y = ½x - ⅕

Find the equation of a line which…

a) has a slope of - ⅖ and crosses the y-axis at +4

b) crosses the y-axis at -2 and is parallel to: y = ½x – 6

c) crosses the y-axis at +7 and is perpendicular to y = 3x + 2

Find the equation of a line which…

d) crosses the y-axis at +7 and passes through the point (-8, 1)

e) passes through the points (-4, 0) and (4, 6)

Applying Pythagorean theorem

1) Solve for the missing side in the triangle:

2) A 12 ft ladder is leaning up against a wall. If the base of the ladder is 5 ft from the wall, how far up the wall does the ladder reach?

11.7 cm

6.2 cm

Homework

• Pg. 28 # 1ac, 2abc, 3ce, 5, 6 adefg• Pg. 31 # 1, 3ac, 4bc, 6, 7• Pg. 142 # 1