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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 integers
Review Slope
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
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:
Find the slope of a line through points (3, 4) and (-1, 6).
m 6 4
1 3
2
4
1
2
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
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
Change into standard form.
y 3
4x 2
4 y 4 3
4x 4 2
3x 4y 8
3x 4y 8
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 15
3x 5 0 153x 15
x 5 5,0 is the
-interceptx
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
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
Graphing Lines
*You need at least 2 points to graph a line.
Using x and y intercepts: •Find the x and y intercepts•Plot the points•Draw your line
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
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
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.
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
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
Homework
Homework: p. 78 #7, 11, 17, 19, 23, 25, 27, 29, 31, 33, 37, 39, 43, 49, 53
Challenge - # 62
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