Linear Equations Topics Review

Interactive Algebra

Welcome Back from Winter Break!

• In the linear equations chapter we have learned about linear equations and graphs ( ________ _____ ).

• Today we will review the major concepts you have learned so far.

straight lines

Use your notes…

Important concepts from Linear Equations & Functions section:

• ______________________________________

• ______________________________________

• ______________________________________

STANDARD FORM:

Ax By C

How to tell if an equation is linear:It’s a straight line, no exponents above 1,no variables in the denominator or square root,

Determine if a point is on the graph of a linearequation by plugging in the point.

Review Problems:

1) Write each equation in standard form:

2)

3y 2x 7+ 2x+ 2x

2x 3y 7

x 54

2y(4) (4)

x 5 8y– x – x

x 8y 5

Ax By C

Use your notes…

Important concepts from Using Intercepts:• ______________________________________

• ______________________________________

Use the cover-up method when an equationis in STANDARD FORM.

Ax By CThe cover-up method works because the graphof a line will cross the y-axis when x = 0 ANDit will cross the x-axis when y = 0.

Review Problems (Intercepts):

3) Find the x- and y-intercepts:

4)

4x 12y 24 x-int: 6; (6, 0)y-int: –2; (0, –2)

5y x 15– x– x

x 5y 15x-int: 15; (15, 0)y-int: –3; (0, –3)

StandardForm:

2x 6y 6

Review Problems (Intercepts) Continued:

• Use intercepts to graph the line given by each equation. 5)

2x 66y

x int : 3

(3,0)

y int : 1

(0, 1)

–6y–6yStandard

Form:

Use your notes…

Important concepts from Slope:• _____________

• ______________________________________

Slope formula:

m y2 y1x2 x1

To find the slope from a graph count therise over the run.

_____________m = riserun

** Watch the slope formula song ** http://www.youtube.com/watch?v=g4Jg1N1YRGg

Review Problems (Slope):

6) Find the slope of the line that contains each pair of points:(8, –16) and (4, –4)

x1

y1

x2

y2

_____________m = (– 4)––168 – 4

–124

_____________m = –3

_____________m =

m y2 y1x2 x1

_____________m =

Review Problems (Slope):

7) Find the slope of the line that contains each pair of points:(1, –3) and (–1, –11)

x1

y1

x2

y2

_____________m = (–11)––31 – (–1)

82

_____________m = 4

m y2 y1x2 x1

Review Problems (Slope) Continued:

Find the slope of the line: (No need to write down)7a)

_____________m =

_____________m =

______m =

riserun

1–6

riserun

1–6

16

–

Review Problems (Slope) Continued:

Find the slope of the line: (No need to write down)7b) _____________m = undefined

NOT ZERO!

Review Problems (Slope) Continued:

7c) Find the slope of the line:_____________m = 0

Review Problems (Slope) Continued:

Find the slope of each line.7d)

_____________m =

_____________m =

______m =

riserun

6

3

rise

run

63

2

Use your notes…

Important concepts from Slope Intercept Form:• ___________________

• ______________________________________

• ______________________________________

Slope-intercept form:

y mx b

m = slope of the line; b = y-intercept

** Watch the slope-intercept song (55 secs)** http://www.youtube.com/watch?v=Yw4PdF-aMgA

To write y = mx + b given slope & a point (x, y),plug in the x & y and solve for b!

Review Problems (y=mx+b):

8) Slope = ½ and y-intercept = 9

y mx b

y 1

2x 9

• Write the equation of the line in slope-intercept form:

9) slope = 6, (3, –1) is on the line

Review Problems (y=mx+b):

Solve for the y-intercept (b).Is (3, –1) the y-intercept?

y mx b

yxm

1

6

(3)

b

118b – 18 – 18

19b

y 6x 19

NO!

Review Problems (y=mx+b):

10) Write the equation of the line in slope-intercept form & then graph the equation.

Slope: & (6, –4)

rise: –1run: 3

1

3

y mx b

yxm

4

1

3

(6)

b

4 2b + 2 + 2

2 b

y 1

3x 2

Use your notes…

Important concepts from Point-Slope Form:• _______________

• ______________________________________

• ______________________________________

Point-slope form:

y y1 m(x x1)

m = slope of the line; Given point:

To change from point-slope to slope-intercept,distribute the m and get y by itself.

(x1,y1)

Review Problem (Point-Slope Form):

• Write an equation in slope-intercept form for the line given:

11) slope =3; (5, –1) 12) slope =–2; (–4, 17)

x1

y1

y y1 m x x1

y 13(x 5)

y 13x 15–1 –1

y 3x 16

x1

y1

m 3

m 2

y y1 m x x1

y 17 2(x 4)

y 17 2x 8+17 +17

y 2x 9

Review Problem (Point-Slope Form):

• Write an equation in slope-intercept form for the line through two points:

13) (1, –2) and (3, 10)

Step 1: _______________Formula:

Find the slope.

m y2 y1x2 x1

x2

y2

x1

y1

m 2 101 3

m 12 2

6

Step 2: Substitute the slope and one of the points into the point-slope form:

y y1 m x x1

y 10 6(x 3)

y 10 6x 18+10 +10

y 6x 8