1. 5.3 Writing Linear Equations given Two points
Objective Write an equation of a line given two
points of the line.
Steps:
Find the slope.
y - y
m = 2 1
x - x 2 1

2. Find the y-intercept. Substitute the slope m and the
coordinates of one of the points into the slope-
intercept form, y = mx + b, and solve for the
y-intercept b.
3. Write an equation of the line. Substitute the slope m
and the y-intercept b into the slope-intercept form,
y = mx + b.

3. EXAMPLE
Write an equation of the line that passes through the points
(1, -3) and (3, 5).
(x1,y1)
(x2,y2)
5 – (-3) 8
1. Find the slope.
m =
m = 4
m =
3 – 1 2
2. Find the y-intercept.
Choose one of the ordered pairs.
(Either ordered pair will result in the same y-intercept)
Using (1, -3)
Using (3, 5)
y = mx + b
y = mx + b
-3 = 4(1) + b
5 = 4(3) + b
-3 = 4 + b
5 = 12 + b
-7 = b
-7 = b

4. Substitute the slope and the y-intercept into y = mx + b
m = and b = -7
y = 4x - 7

5. EXAMPLE
Your Turn
1. Find the equation of a line passing through the points
(1, 6) and (3, -4).
Steps
1) Find slope
2) Find y-intercept b
3) Write equation
m = -5
b = 11
Y = -5x +11

6. Two different nonvertical lines are perpendicular if and
only if their slopes are opposite reciprocals of each other.
Negative Reciprocal Examples
Number
Negative Reciprocal 3 -2

7. EXAMPLE
Write the equation of a line perpendicular to the line
y = -2x + 2 and passing through (6, 8).
m = -2.
Perpendicular slope = ½.
Replace ½ into y =mx +b then find b
Use (6,8) for (x,y)
8 = ½(6) + b
8 = 3 + b
5 = b
The equation of the perpendicular line is y = ½ x + 5.

8. EXAMPLE
Try this.
Find the equation of a line perpendicular to the equation
y = -1/3x – 2 and through the point (-2, -3).
m = 3
y = mx + b
-3 = 3(-2) + b
-3 = -6 + b
3 = b
y = 3x + 3

9. Objective 2 2
Modeling a real-life situation.
A camp program charges a registration fee and a daily amount.
If the total bill for one camper was $338 for 12 days and the total
bill for another camper was $506 for 19 days, how much will the
bill be for a camper who enrolls for 30 days?
Identify the independent variable (x) and the dependent
variable (y).
Since part of the bill depends on the number of days, the
independent variable is the number of days.
Write the two ordered pairs. (12, 338) and (19, 506)
The registration fee is the y-intercept (b). This value is not
know.

10. Find the slope and the y-intercept.
(12, 338) (19, 506)
m =
m = 24
y = mx + b
y = 24x + 50
This means that the camper
pays $24 each day and a
registration fee of $50.
338 = 24(12) + b
338 = b
50 = b
If a camper is there for 30 days, find the cost.
y = 24(30) + 50
y =
y = $770