Writing Equations of Lines                                    -- Sections 2.2-2.3 --

    Find the slope of the line that contains the points (-2, 3) and (1,-2).

Solve

Step

Formula for slope given 2 points

(x1, y1) and (x2, y2) 

y2 – y1 = -2 – 3 = -5

x2 – x1 = 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
(1,-2) 
x+ y = - 1

using the points (1,-2) and (2,-3)

-2+ 1 = - 1
-1 = -1

y - y1 = m(x – x1)

 Now use point-slope 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) 
 4x + 3y = -2

m = 3/4 

 The new slope will be the negative reciprocal of 3/4. (Section 2.2) 

4(1) + 3(-2) = -2
4 – 6 = -2

So the new m = -4/3

 Note: 

-2 = -2

y – (-2) = -4/3(x – 1) 

 Now use point-slope form
y - y1 = m(x – x1)

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 - y1 = m(x – x1)

 Now use point-slope form

y – 690 = 30(x – 3)

 Use either point (3, 690) 

y – 690 = 30x – 90

 Solve for y (slope-intercept 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  
    x = 0                         Note this is the y-intercept

    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