Transcript Document

Warm Up
1. Determine if this relation is a function.
2. Find 𝑓(3) if 𝑓 𝑥 =
𝑥 2 −2
.
𝑥−1
3. Find the x-intercept and y-intercept of the graph of
3𝑥 − 5𝑦 = 15. The graph the equation.
4. Find the slope of a line that passes through (3, 5)
and (4, 1).
2.4 Writing Equations of Lines
The slope intercept form of the equation of
a line is 𝑦 = 𝑚𝑥 + 𝑏 where 𝑚 is the
___________ and 𝑏 is the _____________.
Slope-Intercept Form
If you are given the slope and y-intercept
of a line, you can find an equation of the
line by substituting the values of 𝑚 and 𝑏
into the slope-intercept form.
1. 𝑠𝑙𝑜𝑝𝑒
4
, 𝑝𝑎𝑠𝑠𝑒𝑠
3
𝑡ℎ𝑟𝑜𝑢𝑔ℎ 0, 4
Examples
Sometimes it is necessary to calculate the
slope before you can write an equation.
Write an equation in slope-intercept form
for the line.
Try two on your own.
Write an equation of the line.
1. 𝑝𝑎𝑠𝑠𝑒𝑠 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 0, −6 𝑎𝑛𝑑 −4, 10 .
2. 𝑝𝑎𝑠𝑠𝑒𝑠 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 6, −2 𝑤𝑖𝑡ℎ 𝑎 𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 − 4.
Point-Slope Form
The point-slope form of the equation of a line is
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 ), where (𝑥1 , 𝑦1 ) are the
coordinates of a point on the line and 𝑚 is the
slope of the line.
Using a previous example:
Write an equation of a line through 6, −2 with
a slope of 4 using point-slope form.
Try two on your own.
Write an equation of the line.
1. 𝑝𝑎𝑠𝑠𝑒𝑠 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 2, 3 𝑤𝑖𝑡ℎ 𝑎 𝑠𝑙𝑜𝑝𝑒 𝑜𝑓
1
2
2. 𝑝𝑎𝑠𝑠𝑒𝑠 𝑡ℎ𝑟𝑜𝑢𝑔ℎ −2, −1 𝑤𝑖𝑡ℎ 𝑎 𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 − 3.
Standardized Testing
Tests like HSAP or the COMPASS love to ask questions
like this…
Which is an equation of the line that passes
through (-2, 7) and (3, -3)?
A. 𝒚 =
𝟏
𝒙
𝟐
−
𝟑
𝟐
B. 𝒚 = −𝟐𝒙 + 𝟑
C. 𝒚 =
𝟏
𝒙
𝟐
+𝟖
D. 𝒚 = 𝟐𝒙 + 𝟏𝟏
Equations of a Line
What if you are asked to write the equation
of a line given two points?
(-8, -5) and (-3, 10)
What would you have to do?
1.
Find the SLOPE (𝑚)
2.
Use point-slope form to find the equation
Parallel Lines
How do you know if two lines are parallel?
Their SLOPES are the SAME!
𝑦 = 3𝑥 − 1 and 𝑦 = 3𝑥 + 13
𝑦=
1
𝑥
2
and 𝑦 =
1
𝑥
2
+1
Example
Write an equation of a line that passes through
𝟏
(12, 0) and is parallel to 𝒚 = − 𝒙 − 𝟑.
𝟐
Write an equation of a line that passes through (0, 9)
𝟐
and is parallel to 𝒚 = 𝒙 − 𝟏𝟎.
𝟑
Perpendicular Lines
How do you know if two lines are perpendicular?
Their SLOPES are the NEGATIVE RECIPROCALS!
𝑦 = 3𝑥 − 1 and 𝑦 =
𝑦 = −2𝑥 and 𝑦 =
1
− 𝑥
3
1
𝑥
2
+ 13
+1
Example
Write an equation of a line that passes through
𝟐
(5, -6) and is perpendicular to 𝒚 = − 𝒙 + 𝟕.
𝟑
Write an equation of a line that passes through
(6, -1) and is parallel to 𝒚 = 𝟑𝒙 − 𝟐.
Summary
Slope-Intercept Form:
Point-Slope Form:
Equations of a line: (1)
(2)
Parallel Lines:
Perpendicular Lines:
Homework!!! YAY! 
Lesson 2.4
Page 87
#’s 9, 13, 15, 17-19, 23, 24 and 32