The Point-Slope Form Worksheet With Answer Key
ADVERTISEMENT
1
2
3
4
5
6
7190
(4–34)
Chapter 4 Linear Equations in Two Variables and Their Graphs
T H E P O I N T - S L O P E F O R M
4.4
In Section 4.3 we wrote the equation of a line given its slope and y-intercept. In this
I n t h i s
section you will learn to write the equation of a line given the slope and any other
s e c t i o n
point on the line.
Point-Slope Form
G
Point-Slope Form
Parallel Lines
G
2
Consider a line through the point (4, 1) with slope
as shown in Fig. 4.25. Because
Perpendicular Lines
G
3
the slope can be found by using any two points on the line, we use (4, 1) and an
arbitrary point (x, y) in the formula for slope:
y
y
y
2
1
m
3
Slope formula
x
x
2
1
2
(4, 1)
y
1
2
1
2
Let m
, (x
, y
)
(4, 1), and (x
, y
)
(x, y).
1
1
2
2
3
x
4
3
x
– 3
– 2
– 1
1
3
4
– 1
(x, y)
2
y
1
(x
4)
Multiply each side by x
4.
3
– 3
2
Note how the coordinates of the point (4, 1) and the slope
appear in the above
3
F I G U R E 4 . 2 5
equation. We can use the same procedure to get the equation of any line given one
point on the line and the slope. The resulting equation is called the point-slope
h e l p f u l
h i n t
form of the equation of the line.
If a point (x, y) is on a line with
slope m through (x
, y
), then
Point-Slope Form
1
1
y
y
1
m.
The equation of the line through the point (x
, y
) with slope m is
x
x
1
1
1
Multiplying each side of this
y
y
m(x
x
).
equation by x
x
gives us
1
1
1
the point-slope form.
E X A M P L E
1
Writing an equation given a point and a slope
1
Find the equation of the line through ( 2, 3) with slope
, and write it in slope-
2
intercept form.
Solution
Because we know a point and the slope, we can use the point-slope form:
y
y
m(x
x
)
Point-slope form
1
1
1
1
y
3
[x
( 2)]
Substitute m
and (x
, y
)
( 2, 3).
1
1
2
2
1
y
3
(x
2)
Simplify.
2
1
y
3
x
1
Distributive property
2
1
y
x
4
Slope-intercept form
2
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education