4D Writing Equations of Lines
5 STEP PROCESS: Given any two points (x1, y1) and (x2, y2) on a line; i.e. (3, 0) and (5, 4)
Step 0: Write coordinates (if necessary)
Step 1: Find the slope using the slope formula.
y 2  y1
or by looking at the graph
x 2  x1
or
if it is given.
Step 2: Using one of the points (x,y) and your slope, substitute into y=mx + b
Step 3: Solve for b
Step 4: Write the equation of the line in slope-intercept form.
Step 5: Verify with graph
Example 1: Write the equation of a line that has a slope of 3/2 and goes through (-2,1)
Step 1: Slope is given as 3/2
Step 2: Using (-2,1) as (x,y), substitute m=3/2, x=-2, and y = 1
1 = 3/2 (-2) + b
Step 3: 1 = -3 + b
1+3=b
4= b
Step 4: y = 3/2 x +4
Step 5: Verified by graphing 
Example 2: Find the equation of the line that passes through the points (-2, -1) and (2, 1).
Step 1: m = 1  (1)  2  1
(2  2) 4 2
Step 2: Using (2,1) as (x,y) and m= ½, substitute to get 1= ½ (2) + b
Step 3: 1 = 1 + b
1-1 = b so b = 0
Step 4: y = ½ x + 0 or y = ½ x
Step 5: Slope is ½ and y-intercept is 0. (Verified by graph  )
Example 3: Find the equation of the line that passes through the points (-1, 4) and (4, -1).
Step 1:  1  4   5  1
4  (1)
5
Step 2: Using (-1,4) as (x,y) and m= -1, substitute: 4= -1(-1) + B
Step 3: 4 = 1 + B
3=B
Step 4: y = -1x + 3
Step 5: Slope is -1 and y-intercept is 3 (Verified by graph  )
Example 4: Find the equation of the line that passes through the points (3, 4) and (-2, 4).
Step 1: m =
44 0
 0
3  2 5
Step 2: 4 = 0(3) + b
Step 3: 4 = 0 + b
4=b
Step 4: y = 4
Step 5: It’s a horizontal line so y=4
Example 5: Find the equation of the line that passes through the points (2,3) and (2,5)
Step 1: m =
53 2
  undefined
22 0
Step 2: Realize that it’s a vertical line so the answer is x=2
Example 6: Find the equation of the line that passes through y-intercept of 4 and x-intercept of 5.
Step 1: Graph the points to find the slope and to hopefully find the equation
Slope = -4/5 and the y-intercept is 4
Answer: y = -4/5 x + 4
Example 7: Find the equation of the line with an undefined slope and goes through (2,5)
Step 1: Slope is undefined so it’s a vertical line. Therefore x=2
Word Problems: These problems are giving you two points. Find the slope and then use one of the points to write an equation.
Example 8: A 5-minute overseas call costs $7.50 and a 10-minute call costs $15.00. The cost of the call and the length of the
call are related. How long can you talk on the phone if you have $12 to spend?
Step 0: Write coordinate pairs (5,7.50) and (10, 15.00)
Step 1: Find the rate of change:
15  7.5 7.5

 1.5
10  5
5
Step 2: 15 = 1.5(10) + b
Step 3: 15 = 15 + b
0=b
Step 4: y = 1.5x
Call = 1.5*minutes
Answer the question: 12 = 1.5(m)
8 = m so 8 minutes.
Example 9: The cost of a large pizza at Thompson pizza shack is a standard fee plus a certain price for each topping.
A 5-topping pizza is $20 and a 3-topping pizza is $16. Find the cost of a 1-topping pizza
Step 0: (5,20), (3,16)
Step 1: 20  16  4  2 so it costs $2 per topping
53
2
Step 2: 20 = 2(5) + b
Step 3: 20 = 10 + b
10 = b
Step 4: y = 2x + 10 or Cost = 2*topping + 10
Answer the question: C=2*1 + 10 = $12
Practice 1-8) Write the equation of the lines that meets the following conditions:
1.
Slope is 3 and goes through (-2,1)
2. Slope is undefined and goes through (1,4)
3.
Goes through (-1,3) and (-5,1)
4. Goes through (2,3) and (5,3)
5.
Goes through (4,2) and (6,1)
6. (0,4) and (2,5).
7.
The x-intercept is 3 and the y-intercept is -2
8. The x-intercept is 7 and has a slope of -3/5
9. Biologists have found that the number of chirps some crickets make per minute is related to temperature. The relationship is very
close to being linear. When crickets chirp 124 times a minute, it is about 68º F. When they chirp 172 times a minute, it is about 80 º F.
a. Find an equation for the line that models this situation.
b. How warm is it when the crickets are chirping 150 times a minute?
10. Karen rented a car, and after the 2nd day it cost her $19, and after the 6th day it cost her $47.
a. Write the function rule to model the situation. (Find slope first and then the y-intercept)
b. Was there an initial cost to rent the car? If so, what was it?
c. Find the total cost after a full week (7 days).
d. If Karen has $58, how much more does she need in order to rent the car for 10 days?
11. Jacob rented 5 video games for $3.75, and 9 for $6.75.
a. Write the equation that models the situation. (Find slope first and then the y-intercept)
b. How much would it cost to rent 10 video games?
c. Was there an initial cost to rent the games? If so, what was it?
d. Jacob has $4.00, how much more does he need in order to rent 7 video games?
12. Mark rented a bike while at the beach, for 3 days it cost him $11.50, and for 7 days it cost him $21.50.
a. Write a function rule that models the situation. (Find slope first and then the y-intercept)
b. Was there a deposit to rent the bike? If so, how much was it?
c. How much would it cost for Mark to rent it for just 2 days?
d. If Mary wanted to also rent a bike and she had $30, how many days could she rent the bike for?
e. Would she have any money left over? If yes, how much?