Transcript Point-Slope Form

Point-Slope Form
Section 5-4 Part 1
Goals
Goal
• To write and graph linear
equations using point-slope
form.
Rubric
Level 1 – Know the goals.
Level 2 – Fully understand the
goals.
Level 3 – Use the goals to
solve simple problems.
Level 4 – Use the goals to
solve more advanced problems.
Level 5 – Adapts and applies
the goals to different and more
complex problems.
Vocabulary
• Point-Slope Form of a Line
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.
Slope formula
Multiply both sides by (x –
2).
3(x – 2) = y – 1
y – 1 = 3(x – 2)
Simplify.
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.
Point-Slope Form
y – y1 = m(x – x1)
y-coordinate
x-coordinate
slope
(x1, y1) represents a
specific point and
(x, y) represents any
point.
Example: 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.
A.
B.
C.
Your Turn:
Write an equation in point-slope form for the line with the given slope
that contains the given point.
a.
b.
slope = 0; (3, –4)
y – (–4) = 0(x – 3)
y + 4 = 0(x – 3)
Example: Writing Linear
Equations Using Point-Slope Form
Write an equation in slope-intercept form for the line with slope 3
that contains (–1, 4).
Step 1 Write the equation in point-slope form:
y – y1 = m(x – x1)
y – 4 = 3[x – (–1)]
Step 2 Rewrite the equation in slope-intercept form by solving for y.
y – 4 = 3(x + 1)
y – 4 = 3x + 3
+4
+4
y = 3x + 7
Rewrite subtraction of negative
numbers as addition.
Distribute 3 on the right side.
Add 4 to both sides.
Your Turn:
Write an equation in slope-intercept form for the line with slope
that contains (–3, 1).
Step 1 Write the equation in point-slope form:
y – y1 = m(x – x1)
Continued
Step 2 Rewrite the equation in slope-intercept form by
solving for y.
Rewrite subtraction of negative
numbers as addition.
Distribute
+1
+1
on the right side.
Add 1 to both sides.
Point-Slope Form and
Graphing
In Lesson 5-3, you saw that if you know the slope
of a line and the y-intercept, you can graph the line.
You can also graph a line if you know its slope and
any point on the line.
Example: Graphing Using
Point-Slope form
Graph the equation
y5
1
2
What is the ordered pair?
(x1, y1) = (2, 5)
What is the slope?
m=
1
2
x  2 
Your Turn:
Graph the equation
y5 
2
3
What is the ordered pair?
(x1, y1) = (-2, 5)
What is the slope?
m= 2
3
x  2 
Example: Graphing Given a
Point and the Slope
Graph the line with the given slope that contains the given point.
slope = 2; (3, 1)
Step 1 Plot (3, 1).
Step 2 Use the slope to move from (3, 1) to
another point.
Move 2 units up and 1 unit right
and plot another point.
Step 3 Draw the line connecting the two points.
1
•
2
• (3, 1)
Example: Graphing Given a
Point and the Slope
Graph the line with the given slope that contains the given point.
slope =
; (–2, 4)
4
Step 1 Plot (–2, 4).
3
(–2, 4)
Step 2 Use the slope to move from (–2, 4) to
another point.
Move 3 units up and 4 units right
and plot another point.
Step 3 Draw the line connecting the two points.
•
(2, 7)
•
Example: Graphing Given a
Point and the Slope
Graph the line with the given slope that contains the given point.
slope = 0; (4, –3)
A line with a slope of 0 is horizontal.
Draw the horizontal line through (4, –3).
•
(4, –3)
Your Turn:
Graph the line with slope –1 that contains (2, –2).
Step 1 Plot (2, –2).
Step 2 Use the slope to move from (2, –2) to
another point.
(2, –2)
−1
Move 1 unit down and 1 unit right
and plot another point.
Step 3 Draw the line connecting the two points.
•
1
•
Joke Time
• Why do milking stools only have three legs?
• Because the cow’s got the udder!
• What did the mother Buffalo say when her boy
left for college?
• Bye-Son!
• What do you do with a sick boat?
• Take it to the doc.
Assignment
• 5-4 Part 1 Exercises Pg. 340: #6 – 18 even