2.5Writing Equation of a Line

Sept 9, 2013

Example 1 Write an Equation Given a Graph

Write an equation of the line in slope intercept form.

Solution:1. Pick any 2 points on the line and

determine the slope

m =

2. Determine b (y-int) on the graph.b = -2

Answer:

3

5

y-int(b)

Writing Equation of a line given:

1. Substitute the x-coordinate of the point for x and y-coordinate for y and the slope for m in the equation y= mx + b.

2. Solve for b. 3. Now that you have b and m,

write the equation of the line in y = mx + b

slope and a point

Example 2Write an equation of the line that passes through (4, 2) and

has a slope of .4

1–

=y 341

– x +

y = mx + b2 = -¼ (4) + b2 = -1 + b+1 +13 = b

Substitute 2 for y, 4 for x and -¼ for m

Simplify

Solve for b

Checkpoint

Write an equation of the line that passes through the given point and has the given slope. Write your equation in slope-intercept form.

ANSWER 5= 2xy +

7= 3xy +–ANSWER

14= 5xy +ANSWER

=y3

2x 1–ANSWER

Extra Examples

1. ( )31,– =m 2,

2. ( )4, 5– =m 3–,

( )42,– =m 53. ,

( )3,– 3– =m3

24. ,

Find the Equation of the LineGiven Two Points

●Calculate the slope of the two points.

●Use one of the 2 points and the slope to substitute into the Slope-intercept equation and solve for b.

●Write your equation in y=mx + b form.

1

2 1

2=y y

mx x

Example

●Write the equation of the line that goes through the points (3, 2) and (5, 4).

1

2 1

4 2

5 32

12

2=y y

mx x

m

m

x y

- 3 - 3-1 = b

-5 - 5-1 = b

𝑦=𝑥−1

x y

𝑦=𝑚𝑥+𝑏

Extra Example

●Write the equation of the line that goes through the points (4, -1) and (2, -2).

𝑦=12𝑥−3

Extra Example

●Write the equation of the line that goes through the points (6, -3) and (-4, 2).

𝑦=−12𝑥

Homework:

2.5 p.97 #21-23, 25-30, 44-48

Quiz 2.3-2.4 Wednesday