Transcript Linear Eq - Everett School District

2-4 More Linear Equations
Point Slope Form
Objective:
I can write and graph a linear
function in point slope form
Point Slope Form
Slope Formula:
( x  x1 )
y2  y1
m
x2  x1
y  y1
 m ( x  x1 )
x  x1
Slope
y  y1  m( x  x1 )
Examples
Point (2, 3) Slope: 4
y
3  4 (x  2 )
Point (-3, -7) Slope:
y
+
7

2
3
(x 
+
3
2
3
)
Point (-6, 5) Slope: -2
Point
(x1, y1)
y
+6 )
5  -2 ( x 
Write an equation given two points
Equation for the line that passes through
(3, 2) and (5, 8)
82
6
m

3

1. Find the slope.
53
2. Choose 1 of the
given points and
substitute into
point-slope form.
2
y  2  3 (x  3 )
Equation for the line
that passes through
(7, 3) and (3, 11)
m
11  3
8
 2

37
4
OR
y  3  2( x  7)
y  8  3 (x  5 )
OR
y  2  3( x  3)
y  2  3x  9
y  3x  7
y  8  3( x  5)
y  8  3x  15
y  3x  7
y  11  2( x  3)
Graphing from point-slope form
Graph the equation:
Graph the equation:
y 3  
y2
Point:
(4, 3)
2
( x  4)
3
Slope:

2
3
Point:
2
( x  4)
5
(4,  2)
Slope:
2
5
Parallel & Perpendicular Lines
Write
a parallel32and
p.86:10-21,
perpendicular
line
35,
through the point (6, 2)
60-62
in slope intercept form
2
y  x5
3
Parallel
3
2
y  2   ( x  6)
Lines:
y  2  ( x  6)
2
3
3
Slopes are
2
y2   x9
y2 x4
2
equal
3
2
y  x2
3
y
3
x  11
2
Perpendicular
Lines:
Slopes are
negative
reciprocal
More Linear Equations
Standard Form
Objective:
I can write and graph a linear
function in standard form.
Three Forms of a linear equation
Slope-Intercept Form: y = mx + b
m = slope
b = y-intercept
Point Slope Form: y – y1 = m(x – x1)
m = slope
(x1, y1) = point
Standard Form: Ax + By = C
where A, B, and C are integers.
- meaning no fractions or decimals.
𝑦 = 23𝑥+5
𝑦 − 9 = 23(𝑥−6)
2𝑥 − 3𝑦 = −15
Standard Form to
Slope-Intercept Form
3𝑥 + 5𝑦 = 15 Solve
for y!
5𝑦 = −3𝑥 + 15
𝑦 = −35𝑥 + 3
Slope-Intercept Form
to Standard Form Ax + By = C
𝑦=
7
−5 𝑥
+3
5( 75𝑥 + 𝑦 = 3 )
7𝑥 + 5𝑦 = 15
𝑦 = 32𝑥 + 7
−3𝑥 + 2𝑦 = 14
Add or Subtract mx
from both sides.
No fractions
or decimals
Multiply to eliminate
denominators.
3𝑥 − 2𝑦 = −14
Graphing a standard form equation
Find and graph the intercepts.
x-intercept
y-intercept
𝐴𝑥 + 𝐵𝑦 = 𝐶
𝐴𝑥 + 𝐵𝑦 = 𝐶
𝐴𝑥 + 𝐵(0) = 𝐶 𝐴(0) + 𝐵𝑦 = 𝐶
𝐴𝑥 = 𝐶
𝐵𝑦 = 𝐶
𝑥 = 𝐴𝐶
𝑦 = 𝐵𝐶
3x + 5y = 15
15
15
y=
x=
5
3
x=5
y=3
___________
_________
A runner is participating in a 10-kilometer road race
and she is currently at the halfway point. She looks
at her watch and notices that it has taken her exactly
twenty five minutes to get to this point. Assume that
she has run at a constant rate and will complete the
race at this same rate.
Write an equation to represent the distance she has run from where she
is now.
x = Time (minutes)
Slope-intercept Form
y = Distance from 5 km (km)
Running Rate:
5km
25 min
y  mx  b
 0 .2
Starting point: 5 (y-intercept)
y  0.2 x  5
After a water main break, a large building’s basement was
flooded to the ceiling. The local fire department provides
two pump trucks to pump the water out. The first truck can
pump 25 cubic feet of water per minute and the second truck can
pump 32 cubic feet of water per minute. The building is a rectangular prism,
measuring 150 feet long, 120 feet wide and 10 feet deep.
p. 86:22-31, 36-41
If both trucks are used for different amounts of time to pump out the
basement, write an equation to represent this situation.
Time spent pumping
Amount of
water 1st Truck
+
Amount of
= Total
water 2nd Truck
x = First Truck
y = Second Truck
Standard Form
25 x  32 y  180,000