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Lesson 2-2
Linear Equations
• Linear function – a function whose graph is a
line.
• A linear function is represented by a linear
equation.
ex) y = 2x + 3
A solution of a linear equation is an ordered pair.
y = 3x + 2
Because the value of y depends on the value of x,
y is called the DEPENDENT VARIABLE and
x is called the INDEPENDENT VARIABLE
• When graphing a linear equation make a
t-chart.
• y = 3x + 2
• To be sure you didn’t make a mistake graph at
least three points.
• y-intercept – point where the line crosses the
y axis.
• What is the value of x at the y-intercept.
• x-intercept – point where the line crosses the
x axis.
• What is the value of y at the x-intercept.
Slope
Slope = vertical change
= rise = y2 – y1
horizontal change
run
x 2 – x1
Find the slope of the line that goes through the
points ( -2, -2) and (4, 2)
• Standard Form of a linear equation – is in the
form
Ax + By = C
• A must be positive.
• A, B, and C are integers.
You can graph a linear equation in Standard
Form by using the intercepts
• When an equation is in standard form the
slope = -A/B
• 2x + 3y = 7
• Slope-intercept form
y = mx + b
slope
y-intercept
• Graph from Slope intercept form
– Put the y-intercept on the graph and use the slope
to find other points
• Write in standard form an equation of a line
with slope 2 through (4, -2)
• If you are given two points and asked to write
an equation, Find the slope first, then write
the equation.
• (5,0) (-3, 2)
• Point-Slope Form
The line through point (x1, y1) with slope m has
the equation:
y – y1 = m(x – x1)
• Standard Form: Ax + By = C
• Point Slope Form: y – y1 = m(x – x1)
• Slope Intercept: y = mx + b
Horizontal lines
• m=0
• y is constant
Vertical Lines
• m is undefined
• x is constant
Parallel Lines
m=m
b1 = b2
Perpendicular Lines
• m2 is the opposite reciprocal of m1
• m1 = -1/ m2
• 2-64 even pg 67 - 68