SLOPE AND Y-INTERCEPT FORMLesson 5-3
An equation in the form of ______________ is in ________-_______________ form.
_________ _________
y = mx + b
slopeintercept
slope
y - intercept
y = 4x – 5
y = 4x + 6
-3
y = 2x – 3
3
y = – 2x + 3
II. Write an equation in slope-intercept form for each graph.
-7
(0, -7)
up 1 right 2
Graph (0, -4). Find additional points by going up 2 and right 1.
Graph (0, 5). Find additional points by going up 3 and left 4 OR down 3 and right 4.
5x – 5x + 4y = 8 – 5x
4y = 8 – 5x
(0, 2)
3x – 3x + 2y = 6 – 3x
2y = 6 – 3x
3
V. Write an Equation in Slope-Intercept Form
Suppose you have already saved $50 toward the cost of a new television set. You plan to save $5 more each week for the next several weeks.
What is your starting point? _______
(This will be your _______________.)
What action is being repeated? _____________________
(This becomes the ____________________.)
Write the equation ________________________
$50
y - intercept
Saving $5 each week
slope
y = 5x + 50
Practice: Write an equation in slope-intercept for each situation. 14. A video store charges $15 for a rental card plus $1.50 per rental. 15. A Norfolk pine is 22 inches tall and grows at a rate of 1.4 feet
per year. (Careful, all units must be the same!) 16. A terrier weighs 32 pounds and is on a special diet to lost 3 pounds per month.
17. An airplane at an altitude of 2000 feet ascends at a rate of 750 feet
per mile.
WRITING AN EQUATION GIVEN TWO POINTS. (You must write these on your own paper.)
Directions: Write an equation in slope-intercept form that passes through the line containing the two points given.
M. (-2, 4) and (3, -1)
Step 1: Find the slope.
Step 2: Find the y-intercept (b)
Substitute a point in the equation and solve for “b”
y = mx + b
4= (-1)(-2) + b
4= 2+ b
4 - 2= 2 - 2+ b
2= b
Step 3: Write the equation substituting the value of m and b
y = mx + by = -1x + 2y = -x +2
N. (-2, -1) and (4, 2)
Step 1: Find the slope.
Step 2: Find the y-intercept (b)
Substitute a point in the equation and solve for “b”
y = mx + b
2= (1/2)(4) + b
2= 2+ b
2 - 2= 2 - 2+ b
0= b
Step 3: Write the equation substituting the value of m and b
y = mx + by = ½ x + 0y = ½ x
O. (-6, 5) and (1, 0)
Step 1: Find the slope.
Step 2: Find the y-intercept (b)
Substitute a point in the equation and solve for “b”
y = mx + b
0= (-5/7)(1) + b
0= -5/7+ b
0 + 5/7= -5/7 + 5/7 + b
5/7= b
Step 3: Write the equation substituting the value of m and b
y = mx + by = -5/7x + 5/7
P. (2, -6.9) and (-4, 4.6)
Step 1: Find the slope.
Step 2: Find the y-intercept (b)
Substitute a point in the equation and solve for “b”
y = mx + b
6.9= (1.15)(-2) + b
6.9= -2.3+ b
6.9 + 2.3= -2.3 + 2.3 + b
9.2= b
Step 3: Write the equation substituting the value of m and b
y = mx + by = 1.15x + 9.2
Virtual Nerd on Slope-Intercept Form
Watch these videos to help you understand slope-intercept form.
Homework Tutor - Writing Equations in Slope-Intercept form
Homework Tutor - Graphing a Line Using Slope Intercept Form
Homework Tutor - Equations from Graphs
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