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5-8
Point-Slope Form
Warm Up
Find the slope of the line containing each pair
of points.
1. (0, 2) and (3, 4)
2. (–2, 8) and (4, 2) –1
3. (3, 3) and (12, –15) –2
Write the following equations in slope-intercept
form.
4. y – 5 = 3(x + 2) y = 3x + 11
5. 3x + 4y + 20 = 0
Holt McDougal Algebra 1
5-8
Point-Slope Form
If you know the slope and any point on the line,
you can write an equation of the line by using the
slope formula. For example, suppose a line has a
slope of 3 and contains (2, 1) . Let (x, y) be any
other point on the line.
Substitute into the
slope formula.
Multiply both sides
by (x - 2).
Simplify.
Holt McDougal Algebra 1
5-8
Point-Slope Form
Holt McDougal Algebra 1
5-8
Point-Slope Form
Example 1
Write an equation in point slope form for the line
with the given slope that contains the given point.
y – y1 = m (x – x1)
Holt McDougal Algebra 1
Write the point-slope form.
5-8
Point-Slope Form
You try
Write an equation in point slope form for the line
with the given slope that contains the given point.
slope = –4; (0, 3)
y – y1 = m(x – x1)
Write the point-slope form.
y – 3 = –4(x – 0)
Substitute –4 for m, 0 for x1
and 3 for y1.
y – 3 = –4(x – 0)
Holt McDougal Algebra 1
5-8
Point-Slope Form
You Try
Write an equation in point slope form for the line
with the given slope that contains the given point.
slope = 0; (3, –4)
y – y1 = m(x – x1)
Write the point-slope form.
y – (–4) = 0(x – 3)
Substitute 0 for m, 3 for x1 and
–4 for y1.
y + 4 = 0(x – 3)
Rewrite subtraction of negative
numbers as addition.
Holt McDougal Algebra 1
5-8
Point-Slope Form
Example 2
Graph the line described by the equation.
y – 1 = 2(x – 3)
y – 1 = 2(x – 3) is in the
form y – y1= m(x – x1).
(2,5)
(1,3)
The line contains the point (3, 1).
Step 1 Plot (3, 1).
Step 2 Count 2 units up and 1 unit
right and plot another point.
Step 3 Draw the line connecting the two points.
Holt McDougal Algebra 1
5-8
Point-Slope Form
You Try
Graph the line described by the equation.
y–4=
(x – (–2)) is in the
(-2,4)
form y – y1= m(x – x1).
The line contains the point (–2, 4).
slope: m =
Step 1 Plot (–2, 4).
Step 2 Count 3 units up and 4 units right
and plot another point.
Step 3 Draw the line connecting the two points.
Holt McDougal Algebra 1
(2,7)
5-8
Point-Slope Form
Example 3
Write the equation that describes each line in
slope-intercept form. Slope = 3, (–1, 4) is on the line.
Step 1 Write the equation in point-slope form:
y – y1 = m(x – x1)
y – 4 = 3[x – (–1)]
Step 2 Write the equation in slope-intercept form by
solving for y.
Rewrite subtraction of negative
numbers as addition.
y – 4 = 3(x + 1)
Distribute 3 on the right side.
y – 4 = 3x + 3
+4
+4
Add 4 to both sides.
y = 3x + 7
Holt McDougal Algebra 1
5-8
Point-Slope Form
Example 4
Write the equation that describes the line in
slope-intercept form.
(2, –3) and (4, 1)
Step 1 Find the slope.
Step 2 Substitute the slope and one of the points
into the point-slope form.
y – y1 = m(x – x1)
y – (–3) = 2(x – 2)
Holt McDougal Algebra 1
Choose (2, –3).
5-8
Point-Slope Form
Additional Example 3B Continued
Write an equation in slope-intercept form for
the line through the two points.
(2, –3) and (4, 1)
Step 3 Write the equation in slope-intercept form.
y + 3 = 2(x – 2)
y + 3 = 2x – 4
–3
–3
y = 2x – 7
Holt McDougal Algebra 1
5-8
Point-Slope Form
Additional Example 3C: Writing Linear Equations in
Slope-Intercept Form
Write the equation that describes the line in
slope-intercept form.
Step 2 Find the slope.
Holt McDougal Algebra 1
5-8
Point-Slope Form
Additional Example 3C Continued
Write the equation that describes the line in
slope-intercept form.
Step 3 Write the equation in slope-intercept form.
y = mx + b
Write the slope-intercept form.
y = –4x + 1
Substitute –4 for m and 1 for b.
Holt McDougal Algebra 1
5-8
Point-Slope Form
Classwork/Homework
• Worksheet 6.4 Evens only
Holt McDougal Algebra 1
5-8
Point-Slope Form
Exit Card
Write an equation in slope-intercept form for
the line with the given slope that contains the
given point.
1. Slope = –1; (0, 9)
2. Slope =
y − 9 = –(x − 0)
; (3, –6) y + 6 =
(x – 3)
Write an equation that describes each line the
slope-intercept form.
3. Slope = –2, (2, 1) is on the line
y = –2x + 5
4. (0, 4) and (–7, 2) are on the line y =
Holt McDougal Algebra 1
x+4
5-8
Point-Slope Form
Lesson Quiz: Part II
5. The cost to take a taxi from the airport is a linear
function of the distance driven. The cost for 5,
10, and 20 miles are shown in the table. Write
an equation in slope-intercept form that
represents the function.
y = 1.6x + 6
Holt McDougal Algebra 1