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?
Slope – intercept form
y = mx + b
Point-slope form
y – y1 = m(x – x1)
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 = 3 and the y-intercept is b = – 2.
4
y = mx + b
y=
3
4
x + (– 2)
y=
3
4
x–2
Use slope-intercept form.
Substitute
3
4
Simplify.
for m and –2 for b.
Writing an equation given the slope and y-intercept
m = 3, b = 1
Use slope – intercept form
y = mx + b
y = 3x + 1
y= 3x+1
GUIDED
PRACTICE
Writing
an equation
given the slope and y-intercept
m=–2,b=–4
y = mx + b
y = – 2x + (– 4 )
y = – 2x – 4
GUIDED
PRACTICE
Writing
an equation
3
m=– 4
given the slope and y-intercept
b=
7
2
y = mx + b
7
3
y=– 4 x+ 2
EXAMPLE
2
Writing
an equation given the slope and a point
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.
Let (x1, y1) = (5, 4) and m = – 3.
y – 4 = – 3(x – 5)
y – 4 = – 3x + 15
y = – 3x + 19
GUIDED
PRACTICE
Writing
an
equation given the slope and a point
Write an equation of the line that passes through (– 1, 6) and has a slope of 4.
y – y1 = m(x – x1)
y – 6 = 4(x – ( – 1))
y – 6 = 4x + 4
y = 4x + 10
EXAMPLE
How 3to
write equations of parallel or perpendicular lines
(use the point-slope form)
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.
y – y1 = m2(x – x1)
y – 3 = – 4(x – (– 2))
y – 3 = – 4(x + 2)
y – 3 = – 4x – 8
y = – 4x – 5
EXAMPLE
How3
to write equations of parallel or perpendicular lines
Write an equation of the line that passes through (–2,3)
and is perpendicular to the line y = –4x + 1.
A line perpendicular to a line with slope m = – 4 has a slope of
y – y1 = m2(x – x1)
1
(x – (– 2))
4
1
y – 3 = (x +2)
4
1
1
y–3= x+
4
2
1
1
y= x+
2
4
y–3=
1
4
GUIDED
How PRACTICE
to write
equations of parallel or perpendicular lines
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 – y1 = m2(x – x1)
y – (– 2) = 3(x – 4)
y + 2 = 3(x – 4)
y + 2 = 3x – 12
y = 3x – 14
GUIDED
How PRACTICE
to write
equations of parallel or perpendicular lines
Write an equation of the line that passes through (4, –2)
and is perpendicular to the line y = 3x – 1.
A perpendicular slope is –
1
3
y – y1 = m2(x – x1)
1
y – (– 2) = – (x – 4)
3
1
y + 2 = – (x – 4)
3
1
4
y+2=– x+
3
3
1
2
y=– x–
3
3
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
m=
y2 – y1
x2 –x1
10 – (– 2)
=
2 –5
=
12
–3
=–4
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
GUIDEDHow
PRACTICE
to write
an equation given two points
Write an equation of the line that passes through the given points.
(– 2, 5), (4, – 7)
Find the slope
–7–5
m
=–2
=
4 – (– 2)
Use that slope and one of the two points to find the equation of the line.
y – y1 = m(x – x1)
y – 7 = – 2(x – 4)
y – 7 = – 2 (x – 4)
y + 7 = – 2x + 8
y = – 2x + 1
to write
GUIDEDHow
PRACTICE
an equation given two points
Write an equation of the line that passes through
–8–1
m=
=
–3–6
–9
–9
y – y1 = m(x – x1)
y – (– 8)) = 1(x – (– 3))
y + 8 = 1 (x + 3)
y+8= x+3
y =x–5
=1
(6, 1), (–3, –8)
to write
GUIDEDHow
PRACTICE
an equation given two points
Write an equation of the line that passes through (–1, 2), (10, 0)
0–2
m=
=
10– (– 1)
–
2
11
y – y1 = m(x – x1)
y – 0 = – 2 (x – 10)
11
2
–
y = 11 (x – 10)
20
2
–
y=
x + 11
11
HOMEWORK 2.4
p. 101 #3-16(EOP); 17, 20-25,
30-38, 40-45