Writing Equations of Lines  Sections 2.22.3 
Find the slope of the line that contains the points (2, 3) and (1,2). 
Solve 
Step 


Formula for slope given 2
points
(x_{1}, y_{1}) and (x_{2}, y_{2}) 

y_{2 } – y_{1 }= 2 – 3 = 5 x_{2 } –_{ }x_{1 }= 1 – (2) = 3 
(2, 3) and (1,2) 


Done  
Find the slope of the line that contains the points (1,5) and (4, 2).  
[Solution] 

Find the equation of the line that contains the points (1,2) and (2,3).  
Solve 
Step 
Check 

First find the slope using the slope formula 
You can check each point 
using the points (1,2) and (2,3) 
2+ 1
=  1 

y  y_{1} = m(x – x_{1}) 
Now use pointslope form  
y – (2) = 1(x – 1) 
Use either point (1,2) 
(2,3) 
y + 2 = x + 1 
Get x and y on the same side 
x+ y =  1 
x+ y = 1 
Done Þ General Form 
2+ (3) =  1 
1 = 1 

Find the equation of the line that contains the points (5,3) and (4,1).  
[Solution] 

Find the equation of the line that contains the point
(1,2) and is perpendicular to the line 3x – 4y = 2 

Solve 
Step 
Check 
3x – 4y = 2 
First find the slope of by solving for y 
You can check one point 
4y = 3x – 2 
Subtract 3x from both sides  
y = (3/4)x + 2/4 
Divide by 4 
(1,2) 
m = 3/4 
The new slope will be the negative reciprocal of 3/4. (Section 2.2) 
4(1) + 3(2)
= 2 
So the new m = 4/3 
Note: 
2 = 2 
y – (2) = 4/3(x – 1) 
Now use pointslope form y  y_{1} = m(x – x_{1}) 

3(y + 2) = 3[4/3(x – 1)] 
Multiply by 3  
The fraction is gone now.  
3y + 6 = 4(x – 1) 

3y + 6 = 4x + 4 
Get x and y on the same side  
4x + 3y = 2 
Done Þ General Form  
Find the equation of the line that contains the point
(1,3) and is perpendicular to the line 3x + 5y = 6 

[Solution] 


A rare baseball card is expected to be worth $ 690 after 3 years and $780 after 6 years. What will the baseball card be worth after 8 years? How much is the card worth today? 
This is an appreciation
problem because the card is worth more after 6 years than after 3
years. Let x = years and y = value in dollars 

Solve 
Step 

(3, 690) and (6,780) 
We have two points  

First find the slope using the slope formula  
using the points (3,690) and (6,780)  
y  y_{1} = m(x – x_{1}) 
Now use pointslope form  
y – 690 = 30(x – 3) 
Use either point (3, 690)  
y – 690 = 30x – 90 
Solve for y (slopeintercept form)  
y = 30x + 600 

After 8 years Þ y = 30(8)
+ 600 = 240 + 600 = $840 x = 8 Worth today Þ
y = 30(0) + 600 = 0 + 600 = $600 

Your car is expected to be worth $ 15,000 after 1 years and $9,000 after 3 years. What will the baseball card be worth after 5 years? How much is the card worth today? 
[Solution] 

Tutorials and Applets by
Joe McDonald
Community College of Southern Nevada