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2.4 Essential Questions
1. What is the point-slope form? 2. How do you write an equation if you are given a
slope and y-intercept?3. How do you write an equation if you are given a
point and a slope?4. How do you write an equation that is parallel or
perpendicular to a given line if you are only given a point?
5. How do you write an equation if you are given two points?
2.4 Write Equations of Lines
y – y1 = m(x – x1)
Point-slope formSlope – intercept form
y = mx + b
Writing an equation given the slope and y-intercept
Write an equation of the line shown.
From the graph, you can see that the slope is m = and the y-intercept is b = – 2. 3
4
y = mx + b Use slope-intercept form.
y = x + (– 2)3
4Substitute for m and –2 for b.
3
4
3
4 Simplify.y = x – 2
m = 3, b = 1
Use slope – intercept form
y = mx + b
y = x + 13
y = x + 13
Writing an equation given the slope and y-intercept
GUIDED PRACTICE
m = – 2 , b = – 4
y = mx + b
y = – 2x + (– 4 )
y = – 2x – 4
Writing an equation given the slope and y-intercept
GUIDED PRACTICE
y = mx + b
m = – b =34
72
y = – x +34
72
Writing an equation given the slope and y-intercept
EXAMPLE 2
Write an equation of the line that passes through (5, 4) and has a slope of – 3.
Because you know the slope and a point on the line, use point-slope form to write an equation of the line.
y – y1 = m(x – x1) point-slope form.
y – 4 = – 3(x – 5)
y – 4 = – 3x + 15
y = – 3x + 19
Writing an equation given the slope and a point
Let (x1, y1) = (5, 4) and m = – 3.
GUIDED PRACTICEGUIDED PRACTICE
Write an equation of the line that passes through (– 1, 6) and has a slope of 4.
y – 6 = 4(x – ( – 1))
y – y1 = m(x – x1)
y – 6 = 4x + 4
y = 4x + 10
Writing an equation given the slope and a point
EXAMPLE 3
Write an equation of the line that passes through (–2,3)
and is parallel to the line y = –4x + 1.
The given line has a slope of m = –4.
So, a line parallel to it has the same slope of –4.
Now you know the slope and a point on the line,
so use the point-slope form with (x1, y1) = (– 2, 3) to write an equation of the line.
How to write equations of parallel or perpendicular lines
y – 3 = – 4(x – (– 2))
y – y1 = m2(x – x1)
y – 3 = – 4(x + 2)
y – 3 = – 4x – 8
y = – 4x – 5
(use the point-slope form)
EXAMPLE 3
Write an equation of the line that passes through (–2,3)
and is perpendicular to the line y = –4x + 1.
How to write equations of parallel or perpendicular lines
A line perpendicular to a line with slope m = – 4 has a slope of1
4
y – y1 = m2(x – x1)
y – 3 = (x – (– 2))14
y – 3 = (x +2)14
y – 3 = x +14
12
y = x +14
12
GUIDED PRACTICEGUIDED PRACTICE
Write an equation of the line that passes through (4, –2) and is parallel to the line y = 3x – 1.
A parallel slope would be 3.
y – (– 2) = 3(x – 4)
y – y1 = m2(x – x1)
y + 2 = 3(x – 4)
y + 2 = 3x – 12
y = 3x – 14
How to write equations of parallel or perpendicular lines
GUIDED PRACTICE
y – y1 = m2(x – x1)
y – (– 2) = – (x – 4)13
y + 2 = – (x – 4)13
y = – x – 13
23
1
3A perpendicular slope is –
43y + 2 = – x +
13
Write an equation of the line that passes through (4, –2) and is perpendicular to the line y = 3x – 1.
How to write equations of parallel or perpendicular lines
How to write an equation given two points
Write an equation of the line that passes through (5, –2) and (2, 10).
First, find the slope
y2 – y1m =
x2 –x1
=
Now you know the slope and two points on the line, so use point-slope form with either given point to write an equation of the line.
y2 – y1 = m(x – x1)
y – 10 = – 4(x – 2)
y – 10 = – 4x + 8
y = – 4x + 18
10 – (– 2)
2 – 5
12– 3
= – 4=
GUIDED PRACTICEGUIDED PRACTICE
Write an equation of the line that passes through the given points.
(– 2, 5), (4, – 7)
Find the slope
m – 7 – 5
=4 – (– 2)
= – 2
How to write an equation given two points
y – y1 = m(x – x1)
y – 7 = – 2(x – 4)
y – 7 = – 2 (x – 4)
y = – 2x + 1
y + 7 = – 2x + 8
Use that slope and one of the two points to find the equation of the line.
GUIDED PRACTICEGUIDED PRACTICE
(6, 1), (–3, –8)
m =– 8 – 1
– 3 – 6
– 9– 9
= = 1
How to write an equation given two points
Write an equation of the line that passes through
y – y1 = m(x – x1)
y = x – 5
y – (– 8)) = 1(x – (– 3))
y + 8 = 1 (x + 3)
y + 8 = x + 3
GUIDED PRACTICE
(–1, 2), (10, 0)
m =0 – 2
10– (– 1)
211
= –
How to write an equation given two points
Write an equation of the line that passes through
y – y1 = m(x – x1)
y – 0 = (x – 10) 211–
y = (x – 10)211–
y = 211– x + 20
11
HOMEWORK 2.4p. 101 #3-16(EOP); 17, 20-25,
30-38, 40-45
