1.3/1.4 Linear Equations, Direct Variation and Proportion

Warm-up (IN)

Learning Objective: to write equations given 2 points and that are parallel and perpendicular to a given line. And, to write and solve direct variation equations and proportions.

1. Find the slope of the line containing the points (-1,12) and (5,-6).

2. Write the equation in slope-intercept form of the line that has a y-intercept of 0 and a slope of -1.

3. Solve the equations:

-3

3a. 8

4x

y x

b. 204

k

5c.

2 8

n

32

3z 80k 1.25n

Ex 1 – Write an equation in slope-intercept form for the line in the Warm-up #1.

Notes

y mx b 3m ,x y 1,12

12 3 1 b

12 3 b

9 b

y 3x 9

Ex 2 – Write an equation in point-slope form for the line with slope ¾ and contains the point (-12,2)

1 1y y m x x

y 2 3

4 x 12

Point-slope form is often used in Calculus!

If 2 lines have the same slope, thenthey are parallel

If 2 lines are perpendicular, then their slopes are

opposite reciprocals

Ex 3 – Write an equation for the line

a. through (-2,7), that is parallel to 3 4y x

m3 y mx b 7 2 3 b

7 6 b

13 b

y 3x 13

b. through (4,-3), that is perpendicular to 4 5y x

m 1

4

y mx b 3 4

1

4

b

3 1 b

2 b

y 1

4x 2

Direct Variation equation -

y kx• y varies directly as x

• as x increases, y increases at a constant rate

d rt s rh

Other examples?

Measure circular objects and complete the table

Diameter (x) Circumference (y) Circ/Diam (y/x)

y x

C d

Ex 4 – Find the variation constant if y=15 and x=3

y kx15 k 3

5k

Ex 5 – Rita rides her bike 4 miles in 20 minutes. How long will it take to ride 9 miles?

d rt4

Need to find rate

20r

r 1

5

1

5d t

19

5t

45 t

Or…Set up a proportion

min

miles

utes

4

20

9

x

4x 18045x

Ex 6 – solve the proportion

2 1 3

5 7

a a

15a 14a 7a 7

HW – p. 26 #10,11,22,29,35,38,43,48,78 p. 33 #10,14,17,30,32,37,46,64

Out – when are linear equations not direct variations? How are the graphs different?Summary – I understand…ORI’m confused about…

Challenge Probs. For EC…