Lesson 4 ­ REVISED Review of Equations of Lines complete.notebook
March 06, 2020
March 6, 2020
Review of Equations of
Lines
WARM UP:
a) Find the midpoint of: (8 , ­2) and (­5 , 7)
b) A(­2,­6) is the endpoint and B(0 , 3) is the midpoint on line AC. Find
the endpoint C.
Review: Slope of a Line
Calculate the slope of the line joining points
(­6, 4) and (2, ­8).
Using the graph....
m = rise
run
Using the ordered pairs....
m = y2 ­ y1
x2 ­ x1
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Lesson 4 ­ REVISED Review of Equations of Lines complete.notebook
March 06, 2020
Review: Equations of Lines
There are two main forms of the equation of a line.
1) slope and y­intercept form: y = mx + b
2) standard form:
Ax + By + C = 0
• all terms are on one side of the
equation
• the coefficient of x must be positive
• NO fractions .
Finding the Equation of a Line
To write the equationof a line,
we need to know...
*
*
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Lesson 4 ­ REVISED Review of Equations of Lines complete.notebook
March 06, 2020
The Various Scenarios...
1) THE SLOPE AND Y­INTERCEPT ARE KNOWN.
To determine the equation of the line,
substitute directly into y = mx + b.
eg. a) The slope is ­4 and the y­intercept is 9.
b) The slope is ½ and the y­intercept is ­7.
2) THE SLOPE AND A POINT ON THE LINE ARE KNOWN.
• Find the y­intercept by substituting the point and slope into
y = mx + b and solve for b.
• Once both the slope and y­intercept are known, substitute
directly into y = mx + b.
eg. a) The slope is 3 and point (­1, 4) is on the line.
b) The slope is ­¾ and point (2, ­7) is on the line.
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Lesson 4 ­ REVISED Review of Equations of Lines complete.notebook
March 06, 2020
3) TWO POINTS ON THE LINE ARE KNOWN.
• Find the slope using, m =
• Find the y­intercept by substituting the slope and one point
into y = mx + b and solve for b.
• Once both the slope and y­intercept are known, substitute
directly into y = mx + b.
eg. a) The line passes through (­6, ­2) and (4, 3).
b) The line passes through (7, ­10) and (3, 8).
Review: Horizonatal
and Vertical Lines
Horizontal Lines
• written in the form y = #
• slope is equal to ZERO
Determine the equation of a horizontal line through
the point (2, ­7).
Vertical Lines
• written in the form x = #
• slope is UNDEFINED
Determine the equation of a vertical line through the
point (2, ­7).
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Lesson 4 ­ REVISED Review of Equations of Lines complete.notebook
March 06, 2020
Review: Parallel and
Perpendicular Lines
Parallel lines have the same slope.
Perpendicular lines have slopes that are
negative reciprocals.
eg.
eg.
1. Determine the equation of a line that is parallel to
3x ­ 5y = 10 and passes through the point (4, ­5).
2. Determine the equation of the line that is perpendicular to
x ­ 3y ­ 1 = 0 and passes through the point (­3, 1).
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Lesson 4 ­ REVISED Review of Equations of Lines complete.notebook
March 06, 2020
Review:
• Handout…Finding the
Equation of a Line
Equations of Lines
**Quiz ... Monday**
­ length of line
­ equation of circle
­ midpoint of a line
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