Page 143 - Math Course 3 (Book 1)

Equations in Different Forms
Mo. 4

Lesson 5 Let’s Begin

KEY CONCEPTS:
1. Write the equation of a line in point-slope Write an Equation Given Slope and a Point
form.
2. Write linear equations in different forms.
Example

MO. 4 - L5a Write the point-slope form of an equation for a line
3
that passes through (–2, 0) with slope – 2
Equations: Point-Slope Form

Vocabulary A-Z
Let us learn some vocabulary

y – y = m(x – x ) Point-slope form
1
1
point-slope form 3
y – 0 = – [x –(–2)] x – y = (–2, 0)
The equation generated using the coordinates of a 2 1 1
known point and the slope of the line. It is written 3
in point-slope form. y = – (x + 2) Simplify.
2

Points slope Form
(if you know a point and the slope)
3
Answer The equation is y = – (x + 2)
y – y = m( x – x ) 2
1
1
m = slope
(x – x ) = any point on the line
1
Key Concept Real World Example

Charlie is flying from San Diego, California, to
Point–Slope Form Washington D.C., for vacation. After 1.5 hours, his
plane has traveled 810 miles. If the average speed
of travel is 540 miles per hour, write the equation of
Words The linear equation y – y = m(x – x ) is the line in point-slope.
1
1
written in point-slope form, where (x , y )
1
1
is a given point on a non-vertical line and Let x represent hours and y represent miles. The
m is the slope of the line. average speed of travel is the slope, so m = 540.
Symbols y – y = m(x – x ) Let (x1, y1) = (1.5, 810).
1 1
y
Model given point y – y = m(x – x ) Point-slope form
1
1
y – 810 = 540(x – 1.5) (x , y ) = (1.5, 810).
(x, y) 1 1
(x , y )
1 1 The equation y – 810 = 540
Answer
(x – 1.5) represents his trip.
0 x
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