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…