Download Holt McDougal Algebra 1 5-8

5-8
Point-Slope Form
Objectives
Graph a line and write a linear equation using
point-slope form.
Write a linear equation given two points.
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
Additional Example 1A: Writing Linear Equations in
Point-Slope Form
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
Additional Example 1B: Writing Linear Equations in
Point-Slope Form
Write an equation in point slope form for the line
with the given slope that contains the given point.
slope = –4; (0, 3)
Holt McDougal Algebra 1
5-8
Point-Slope Form
Additional Example 1C: Writing Linear Equations in
Point-Slope Form
Write an equation in point slope form for the line
with the given slope that contains the given point.
slope = 1; (–1, –4)
Holt McDougal Algebra 1
5-8
Point-Slope Form
Check It Out! Example 1b
Write an equation in point slope form for the line
with the given slope that contains the given point.
slope = 0; (3, –4)
Holt McDougal Algebra 1
5-8
Point-Slope Form
In Lesson 5-7, you graphed a line given its
equation in slope-intercept form. You can
also graph a line when given its equation in
point-slope form. Start by using the equation
to identify a point on the line. Then use the
slope of the line to identify a second point.
Holt McDougal Algebra 1
5-8
Point-Slope Form
Additional Example 2A: Using Point-Slope Form to
Graph
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
Additional Example 2B: Using Point-Slope Form to
Graph
Graph the line described by the equation.
Holt McDougal Algebra 1
5-8
Point-Slope Form
Additional Example 2C: Using Point-Slope Form to
Graph
Graph the line described by the equation.
y + 3 = 0(x – 4)
Holt McDougal Algebra 1
5-8
Point-Slope Form
Check It Out! Example 2a
Graph the line described by the equation.
y + 2 = –(x – 2)
Holt McDougal Algebra 1
5-8
Point-Slope Form
Additional Example 3A: Writing Linear Equations in
Slope-Intercept Form
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
Additional Example 3B: Writing Linear Equations in
Slope-Intercept Form
Write the equation that describes the line in
slope-intercept form.
(2, –3) and (4, 1)
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.
Holt McDougal Algebra 1
5-8
Point-Slope Form
Check It Out! Example 3a
Write the equation that describes the line
in slope-intercept form.
Holt McDougal Algebra 1
5-8
Point-Slope Form
Check It Out! Example 3b
Write an equation in slope-intercept form for
the line through the two points.
(1, –2) and (3, 10)
Holt McDougal Algebra 1
5-8
Point-Slope Form
Additional Example 4: Using Two Points Find
Intercepts
Write an equation in slope-intercept form for
the line through (10, –3) and (5, –2).
Holt McDougal Algebra 1
5-8
Point-Slope Form
Check It Out! Example 4
Write an equation in slope-intercept form for
the line through the two points.
(2, 15) and (–4, –3)
Holt McDougal Algebra 1
5-8
Point-Slope Form
Lesson Quiz
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