Math 8H

Algebra 1 Glencoe McGraw-Hill JoAnn Evans

Standard Form

And

Word ProblemsHeath text, section 5.5

Slope-Intercept Form of a Linear Equation:

y = mx + b

Point-Slope Form of a Linear Equation:

y – y1 = m(x – x1)

Standard Form of a Linear Equation

Ax + By = C

Remember that in Standard Form, both variable terms are on the left side of the equal sign and the constant

term is on the right side. Another feature of the Standard Form is that all coefficients are integers.

Write an equation in standard form of the line that passes through the point and has the given

slope.

6m),4,2(

8 b

b)2(64

4 12 b

6x y 8

y 6x 8

bmxy

Using y = mx + b 6m),4,2(

y 4 6x 12

y 4 6 x ( 2)

y 4 6(x 2)

6x y 8

y 6x 8

1 1y y m(x x )

1 1Using y y m(x x )

Candy corn costs $2 per pound at the candy store and M&Ms cost $3 per pound. With $30 to spend, what are

the different amounts of the two candies that you can buy?

Let x = # pounds of M & Ms

Let y = # pounds of candy corn

Let 3x = VALUE of the M & Ms

Let 2y = VALUE of the candy corn

Value of the M &

Ms+ Value of the candy

corn=Total Cost

3x + 2y = 30

0 2 4 6 8 10 12 14 16

M & M’s (in pounds)

Can

dy C

orn

(i

n

pou

nd

s)

16

14

12

10

8

6

4

2

Find the x- and y-intercepts.

3(0) + 2y = 30

y = 15

(all candy corn, no M &

M’s)

3x + 2(0) = 30

x = 10

(all M&Ms, no candy corn)

Each point on the line represents a combination of the 2 candies that

would have a total cost of $30.Name some of the combinations.

Suppose you had $6.00 to buy bananas and apples. Bananas cost $0.49 per pound and apples cost $0.34 per pound. Write a linear equation that

represents the different amounts of fruit you could buy.

Let x = weight of bananas

Let y = weight of apples

Let 49x = VALUE of bananas

Let 34y = VALUE of apples

Value of bananas +

Value of apples = Total price

49x + 34y = 600

One possibility is that you could buy 10 pounds of bananas. How many pounds of apples would

then be possible to buy?

49x + 34y = 600

49(10) + 34y = 600

490 + 34y = 600

-490 -490

34y = 110

y 3.2 lb of apples

You are running for class president and have $48 to spend on publicity for your campaign. It costs $2 to

make a campaign button and $1.20 to make a poster. Write an equation that represents the different

numbers of buttons, x, and posters, y, that you could make.

Let x = # of buttons

Let y = # posters

Let 2x = VALUE of the buttons

Let 1.2y = VALUE of the posters

Value of buttons

+ Value of posters

= Total Cost

2x + 1.2y = 4820x + 12y =

4805x + 3y = 120

0 4 8 12 16 20 24 28 32 36 40

buttons

poste

rs

32

28

24

20

16

12

8

4

Should a line be drawn to connect the intercepts? Think for

a minute to form an opinion.

36

40

0

0

24

40

x y

This equation is in standard form. What can we learn by looking at it in slope-intercept form?

3y 5x 120

5x 3y 120

Look for this pattern in the table of values. The change in y is down 5; the change in x is up 3.

y-intercept

3y 5 120x

3 3 3

5y x 40

3

0 40

3 35

x y

-5+3

0 4 8 12 16 20 24 28 32 36 40

buttons

poste

rs

32

28

24

20

16

12

8

4

The slope you just found shows how the change in y and the

change in x can help to find other possible combinations of buttons

and posters.

36

40

5

0

0

12

15

18

21

24

40

20

15

10

9 25

6 30

3 35

x y

-5+3

Dogs sell for $40 and cats sell for $35 at Pets-R-Us. Sales figures for the busy holiday shopping season

showed that the store received $840 total for dog and cat sales in one weekend. Write an equation to

describe the sales that weekend of dogs, x, and cats, y.

Let x = # dogs

Let y = # cats

Let 40x = VALUE of dogs

Let 35y = VALUE of cats

Value of dogs + Value of cats = Total Cost

40x + 35y = 840

8x + 7y = 168

0 3 6 9 12 15 18 21 24 27 30

24

21

18

15

12

9

6

3

27

30

0 24

14 8

7 16

x y

Put the equation in slope-intercept form.

8y x 24

7

-8+7

Using the slope information, find more combinations of dogs and

cats.

Should the x- and y-intercepts be connected in

this case? 21 0

No! Who wants half a dog or two-

thirds of a cat?