FINDING AN EQUATION

GIVEN TWO POINTS

Chapter 5.1

FINDING AN EQUATION Lesson Objective: NCSCOS 4.01 –

Students will know how to find the slope of a lineStudents will know how to find the equation

of a line given 2 points

FINDING AN EQUATION Example 1: Find the equation of a line

that passes through the points (3, 5) and (6, 2)

The equation of a line is:

We always have to find the slope first!

y = mx + b

FINDING AN EQUATION The equation to find slope is:

In order to find slope, we’re going to need to ordered pairs (points)

m =y2 – y1

x2 – x1

_____

FINDING AN EQUATION Find the slope of the line using the two

points (3, 5) and (6, 2) To solve this problem, we have to label

our two points. It doesn’t matter which point you label

x1 and which one x2

(3, 5) (6, 2)X1,Y1 X2,Y2

FINDING AN EQUATION

Plug the points into the slope equation

(3, 5) (6, 2)X1,Y1 X2,Y2

_____x2 – x1

y2 – y1

m =2 - 56 - 3

FINDING AN EQUATION

Simplify the top and the bottom Simplify the fraction

(3, 5) (6, 2)X1,Y1 X2,Y2

_____m =2 - 56 - 3-33

-1

FINDING AN EQUATION

m = -1, so the slope for these two points is -1

(3, 5) (6, 2)X1,Y1 X2,Y2

m =-1

FINDING AN EQUATION Once you know slope, plug it into the

equation:

To find b we have to plug in one of the points

It doesn’t matter which point, if they are both on the same line, they will both work for this equation

y = mx + by = -1x + b

FINDING AN EQUATION Plug in one of the points

y = -1x + b

•Multiply on the right side•Add 3 to both sides•Plug b back into the equation

5 = -1(3) + b 5 = -3 + b

+3 +38 = by = -1x +

8

FINDING AN EQUATION

1. (1, 3), (2, 7)2. (6, 3), (7, -4)3. (6, -2), (5, -4)4. (7, -4), (4, 8)5. (12, 2), (-6, 5)

Find the equation using the following points

Your turn

FINDING AN EQUATION

1. (1, 3), (2, 7)2. (6, 3), (7, -4)3. (6, -2), (5, -4)4. (7, -4), (4, 8)5. (12, 2), (-6, 5)

Find the equation using the following points

Your turn

y = 4x – 1

y = 2x – 14

y = -1/6x + 4

y = -7x + 45

y = -4x + 24

FINDING AN EQUATION Example: Find the equation of the line

A.

In order to find slope, you need two points

Find two points onthe line

Plug the points intothe slope equation

A

(-1, -3)

(1, 1)

FINDING AN EQUATION Label the points and write the equation

(-1, -3)

(1, 1)

m =y2 – y1

x2 – x1

____

(1, 1)(-1, -3)

x1, y1 x2, y2

1 – (-3)

1 – (-1)

1 + 3422

FINDING AN EQUATION Plug the slope into a new equation

y = mx + by = 2x + b•Plug in one of the points•Multiply on the right side•Subtract 2 from both sides•Plug b back into the equation

1 = 2(1) + b

y = 2x – 1

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

FINDING AN EQUATION

1. Find the equation of Line A2. Line B3. Line C4. Line D

D

C

B

A

More Practice

FINDING AN EQUATION

1. Find the equation: (5, 2), (3, -4)

2. (-1, 6), (7, -10)3. (0, 2), (1, 7)4. (-2, -1), (2, 11)5. (10, -1), (4, 2)

Quiz!

FINDING AN EQUATION

1. Find the equation: (5, 2), (3, -4) y = 3x – 13

2. (-1, 6), (7, -10) y = -2x + 4

3. (0, 2), (1, 7) y = 5x + 24. (-2, -1), (2, 11) y = 3x +

55. (10, -1), (4, 2) y = -1/2x

+ 4

Quiz!