2-4 More Linear Equations Point Slope Form

Objective:

I can write and graph a linear function in point slope form

Point Slope FormSlope Formula:

12

12

xx

yym

mxx

yy

1

1)( 1xx )( 1xx

Point (2, 3) Slope: 4Examples

) ( xy 23 4

Point (-3, -7) Slope:

) ( xy + 3+ 7

Point (-6, 5) Slope: -2

) ( xy + 65 -2

3

2

3

2Slope

Point(x1, y1)

)( 11 xxmyy

Write an equation given two pointsEquation for the line that passes through (3, 2) and (5, 8)

1. Find the slope.

2. Choose 1 of the given points and substitute into point-slope form.

35

28

m2

6 3

) ( xy 3 32

OR) ( xy 3 58

)3(32 xy )5(38 xy932 xy 1538 xy

73 xy 73 xySam

e Line?

Equation for the line that passes through (7, 3) and (3, 11)

73

311

m4

8

2

)7(23 xy

OR)3(211 xy

Graphing from point-slope formGraph the equation:

)4(3

23 xy

Point: Slope:

-5 5-5

5

x

y

)3 ,4(3

2

-5 5-5

5

x

y

-5 5-5

5

x

y

-5 5-5

5

x

y

Graph the equation: )4(

5

22 xy

Point: Slope:

-5 5-5

5

x

y

)2 ,4( 5

2

-5 5-5

5

x

y

-5 5-5

5

x

y

-5 5-5

5

x

y

Parallel & Perpendicular Lines

-5 5-5

5

x

y

-5 5-5

5

x

y

Parallel Lines:Slopes are

Perpendicular Lines:Slopes are

53

2 xy

Write a parallel and perpendicular line through the point (6, 2) in slope intercept form

)6(3

22 xy

43

22 xy

23

2 xy

)6(2

32 xy

92

32 xy

112

3 xy

p.86:10-21, 32-35,60-62

equal negative reciprocal

More Linear Equations Standard Form

Objective:

I can write and graph a linear function in standard form.

Standard Form:

Point Slope Form:

Slope-Intercept Form:

Three Forms of a linear equationy = mx + b

y – y1 = m(x – x1)

Ax + By = C

where A, B, and C are integers.- meaning no fractions or decimals.

m = slope b = y-intercept

m = slope (x1, y1) = point

𝑦=23𝑥+5

𝑦− 9=23(𝑥− 6)

2 𝑥−3 𝑦=− 15

Solve for y!

Standard Form to Slope-Intercept Form

No fractionsor decimals

Slope-Intercept Formto Standard Form

Add or Subtract mxfrom both sides.

Multiply to eliminate denominators.

3 𝑥+5 𝑦=15

5 𝑦=− 3𝑥+15𝑦=−

35𝑥+3

𝑦=−75𝑥+3

75𝑥+𝑦=35()

7 𝑥+5 𝑦=15

𝑦=32𝑥+7

3 𝑥− 2 𝑦=− 14−3 𝑥+2 𝑦=14

Ax + By = C

Graphing a standard form equationFind and graph the intercepts.

x-intercept y-intercept

3x + 5y = 15

x = ___________

y = _________

x = y = 3

153

155

5

-5 5-5

5

x

y

-5 5-5

5

x

y

-5 5-5

5

x

y

-5 5-5

5

x

y

𝐴𝑥+𝐵𝑦=𝐶𝐴𝑥+𝐵 (0)=𝐶

𝐴𝑥=𝐶𝑥=

𝐶𝐴

𝐴𝑥+𝐵𝑦=𝐶𝐴(0)+𝐵𝑦=𝐶

𝐵𝑦=𝐶𝑦=

𝐶𝐵

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)

y = Distance from 5 km (km)

Running Rate:

Starting point: 52.0 xy

Slope-intercept Form

min25

5km 2.0

5 (y-intercept)

bmxy

After a water main break, a large building’s basement wasflooded to the ceiling. The local fire department providestwo pump trucks to pump the water out. The first truck canpump 25 cubic feet of water per minute and the second truck canpump 32 cubic feet of water per minute. The building is a rectangular prism, measuring 150 feet long, 120 feet wide and 10 feet deep.

Time spent pumping

x = First Truck

y = Second Truck000,180

If both trucks are used for different amounts of time to pump out the basement, write an equation to represent this situation.

x25 y32

Standard Form

Amount ofwater 1st Truck

+ Amount of water 2nd Truck

= Total

p. 86:22-31, 36-41