Entry Task

LT: I can graph and write equations of lines

2.3 Linear Functions and Slope-Intercept

Form

Learning Target: I can

Graph linear equations I can write equations of lines.

Review of Formulas

Formula for Slope m y2 y1

x2 x1

Ax By C Standard Form

y y1 m x x1 Point-Slope Form

y mx bSlope-intercept Form

*where A>0 and A, B, C are integersLT: I can graph and write equations

of lines

Slope

LT: I can graph and write equations of lines

Examples of linear equations 2x + 4y =8

6y = 3 – x

x = 1

-2a + b = 5

47

3

x y

Equation is in Ax + By =C form

Rewrite with both variables on left side … x + 6y =3

B =0 … x + 0 y =1

Multiply both sides of the equation by -1 … 2a – b = -5

Multiply both sides of the equation by 3 … 4x –y =-21

LT: I can graph and write equations of lines

Examples of Nonlinear Equations

4x2 + y = 5

xy + x = 5

s/r + r = 3

The exponent is 2

There is a radical in the equation

Variables are multiplied

Variables are divided

4x

The following equations are NOT in the standard form of Ax + By =C:

LT: I can graph and write equations of lines

Find the slope of a line through points (3, 4) and (-1, 6).

m 6 4

1 3

2

4

1

2

LT: I can graph and write equations of lines

Write an equation for the line that passes through (-2, 5) and (1, 7):

Find the slope: m 7 5

1 2

2

3

Use point-slope form: y 5

2

3x 2

LT: I can graph and write equations of lines

Change into slope-intercept form and identify the slope and y-intercept.

3x 5y 15

5y 3x 15 5y

5

3x

5

15

53

35

y x 35

5m and b

LT: I can graph and write equations of lines

Change into standard form.

y 3

4x 2

4 y 4 3

4x 4 2

3x 4y 8

3x 4y 8LT: I can graph and write equations

of lines

x-intercepts and y-interceptsThe intercept is the point(s) where the graph crosses the axis.To find an intercept, set the other variable equal to zero.

3x 5y 153x 5 0 15

3x 15

x 5 5,0 is the

-interceptxLT: I can graph and write equations

of lines

Horizontal Lines Slope is zero. Equation form is y = #.

Write an equation of a line and graph it with zero slope and y-intercept of -2. y = -2Write an equation of a line and graph it that passes through (2, 4) and (-3, 4).

y = 4 LT: I can graph and write equations of lines

Vertical Lines Slope is undefined. Equation form is x = #.

Write an equation of a line and graph it with undefined slope and passes through (1, 0). x = 1Write an equation of a line that passes through (3, 5) and (3, -2).

x = 3 LT: I can graph and write equations of lines

Graphing Lines

*You need at least 2 points to graph a line.Using x and y intercepts:

(plug 0 in for x and then y)

•Find the x and y intercepts•Plot the points•Draw your line

LT: I can graph and write equations of lines

Graph using x and y intercepts 2x – 3y = -12

x-intercept2x = -12

x = -6(-6, 0)

y-intercept-3y = -12

y = 4(0, 4)

6

4

2

-2

-10 -5

B: (0, 4)

A: (-6, 0)

B

A

LT: I can graph and write equations of lines

Graph using x and y intercepts 6x + 9y = 18

x-intercept6x = 18

x = 3(3, 0)

y-intercept9y = 18

y = 2(0, 2)

4

2

-2

5

D: (0, 2)

C: (3, 0)

D

C

LT: I can graph and write equations of lines

Graphing Lines

Using slope-intercept form y = mx + b:

•Change the equation to y = mx + b.•Plot the y-intercept.•Use the numerator of the slope to count the corresponding number of spaces up/down.•Use the denominator of the slope to count the corresponding number of spaces left/right.•Draw your line.

LT: I can graph and write equations of lines

Graph using slope-intercept form y = -4x + 1:

Slopem = -4 = -4

1

y-intercept(0, 1)

4

2

-2

-4

5

F: (1, -3)

E: (0, 1)

F

E

LT: I can graph and write equations of lines

Graph using slope-intercept form 3x - 4y = 8

Slopem = 3

4 y-intercept(0, -2)

y = 3x - 2 4

4

2

-2

-4

5

H: (0, -2)

G: (4, 1)G

H

LT: I can graph and write equations of lines

Homework

Homework: p. 78 #7, 11, 19, 23, 25, 27, 29, 33, 37, 39, 43, 49, 53, 58

Challenge - # 62

LT: I can graph and write equations of lines