4-3A Writing Equations in Slope-Intercept Form

Algebra 1 Glencoe McGraw-Hill Linda Stamper

In the previous lesson you wrote direct variation equations.In today’s lesson, when you know the slope and the y-intercept you will be able to write the equation of a line.

The y-intercept is

the y-coordinate of

the point where the line crosses the y-

axis.

x

y

•

Do you remember y-intercept?

bmxy

The linear equation y=mx+b is written in slope-intercept form where m is the slope and b is the y-intercept.

slope y-intercept

bmxy If y = x + 3 then

slope y-intercept

the slope is

and the y-intercept is

Slope is a numerical value – do not include the variable x.

1 3

bmxy If y = 2x – 3 then

slope y-intercept

the slope is

| –

and the y-intercept is

The slope is a numerical

value – do not include the variable x.

2 3-

How to write the equation of a line given the slope and the y-intercept.

Write the slope-intercept form. bmxy

Substitute the slope for m and the y-intercept for b.Simplify – undo the double sign.

Write the equation of the line whose slope is 9 and whose y-intercept is –6 .

bmxy 6x9y 6x9y

Write an equation in slope-intercept form of the line with the given slope and y-intercept.

bmxy

2x7y

2x7y

Example 1

slope: 7 , y-intercept: –2

Example 2

slope:

bmxy

10x43

y

10x43

y

43

, y-intercept: – 10

x

y

# of booksS

hip

pin

g c

osts

(d

ollars

)

12

2 4

An online store charges $3 per order plus $1.00 per book for shipping. Write a linear equation in slope-intercept to model the situation.

0

3456789

6 8 10

Let x represent number of books and y represent cost of shipping.

bmxy

3xy

10

•Find the y-intercept.

Constant rate of change is slope.

The charge per book is the slope, so m = 1.

Example 3 You want to rent a rowboat for a fishing trip. There is an initial fee of $25, plus a $50 daily fee. Write a linear equation for this situation where y represents the cost of renting a rowboat and x represents the number of days rented.

Example 4 Jenny opened a savings account with $200 and plans on saving $100 per month. Write a linear equation for this situation where y represents the savings and x represents the number of months.

Constant rate of change is slope.

x

y

# days

Ren

tal cost

(dollars

)

2550

1 2•

Example 3 You want to rent a rowboat for a fishing trip. There is an initial fee of $25, plus a $50 daily fee. Write a linear equation for this situation where y represents the cost of renting a rowboat and x represents the number of days rented.

0

75100125150175200225

3 4 5

bmxy 25x50y

Find the y-intercept.

Constant rate of change is slope.

x

y

time (months)

savin

gs

(sollars

)

(0,200)10

01 2

•

Example 4 Jenny opened a savings account with $200 and plans on saving $100 per month. Write a linear equation for this situation where y represents the savings and x represents the number of months.

0

300

500

700

900

3 4 5

Find the y-intercept.

bmxy 200x100y

Constant rate of change is slope.

Write 2x – y = -3 in slope-intercept form. The identify the slope and y-intercept.

Write the equation.

3yx2 Rewrite in slope-intercept form (solve for y).

x2 x23 x2y

13x2y

3x2y

Identify the slope and y-intercept.

slope is 2 y-intercept is 3

1 11

You must write the variable

term first. Copy the above in

your spiral notebook!

53 is slope

Example 5 10y5x3 x3 x3

01 x3y5 5

2x53

y

y-intercept is –2

5 5

43

is slope

Example 6 8 y4x3 x3 x3

8 x3y4 4

2x43

y

y-intercept is 2

4 4

Write the equation in slope-intercept form. Then identify the slope and y-intercept.

2x53

y

When a graph clearly indicates the y-intercept and another point on the line, you can use the graph to write an equation of the line.

Recall that the y-intercept is the y-coordinate of the point where the

line crosses the y-axis.

x

y

•

How to write the equation of a line given a graph.

1. Write the slope-intercept form.

2. Locate the y-intercept.

3. Locate another point on the graph to find the slope using the slope ratio. 4. Substitute slope and y-intercept in the

slope intercept form.

5. Simplify if necessary (undo double sign and place negative out front).

bmxy

74

Write the equation of the line shown in the graph using slope-intercept form.

x

y

Write the slope-intercept form.

bmxy

Locate the y-intercept.

Locate another point on the graph.

runrise

m

Substitute the slope and y-intercept in the slope intercept form.

3x4

7y

Simplify - undo double sign. Use good form – place negative out front!

3x47

y

3

•

•

Write the equation of the line shown in the graph using slope-intercept form.

x

y

bmxy

run rise

m3

4

2x43

y

2x43

y

••

Example 7

y-intercept -2

Example 8

x

y

bmxy y-intercept 3

runrise

m 75

3x57

y

3x57

y

•

•

Notice that the scales on the axes are different. In this case it would be difficult to calculate slope by walking the line (counting squares). Instead use the slope formula.

x

y

1

4

–1–4

Scales on the axis different – use slope formula!

Example 9 Write the equation of the line shown in the graph using slope-intercept form.

x

y

14

–1–4

Write the slope-intercept form.

bmxy

Locate the y-intercept. 8

Locate another point on the line.Write the coordinates of both points.

(0,8)

(0,8)(–4,–4)

(–4,–4)Use the slope formula to calculate the slope.

12

12

xxyy

m

)4(0)4(8

4048

412

3

Substitute the slope and y-intercept in the slope intercept form.

8x3y

••

Remember: Scales on the axis different – use slope formula to find the slope!

When the scales on the axes are different, you must use the slope formula. Could you use the slope formula if the scales are the same?

x

y

1

1

–1–1

Yes, but it would be more work!

Write the equation of the line in the graph.

x

y

What axis does the line intercept? y

What is the y intercept? 3-

-3y Write the equation.

•

Write the equation of the line in the graph.

x

y

What axis does the line intercept?x

What is the x-intercept? 4 4 x

•

Example 10

Example 11

x

y

What axis does the line intercept? y

What is the y-intercept? 1 1y

•

Think of some coordinates. (0,1), (0,0), (0,–1), (0,2)

Example 12 What special name is given to the graph of x = 0?

x

y

•••

• y-axis

Example 13 What special name is given to the graph of y = 0?

x

y

Think of some coordinates. (1,0), (0,0), (–1,0), (2,0)

x-axis

••• •

4-A5 Pages 207–208 # 12-23 and Handout A5.