Standard Form

Conversion to and from slope-intercept

100

Convert to standard form: y=x+5

x-y=-5

200

Convert into standard form: y=3x+4.

3x-y=-4

300

Convert into standard form: y=-2x+1.

2x+y=1

400

Convert to slope-intercept: 3x+4y=20.

y=-3/4x+5

500

Convert to slope-intercept: x+10y=15

y=1/10x+2/3

Conversion to and from point-slope

100

Convert to standard form: y+3=2(x-1).

2x-y=5

200

Convert to standard form: y+5=-(x-2)

x+y=3

300

Convert to standard form: y-1=-3(x+2)

3x+y=-5

400

Convert to point-slope form: 3x+4y=12, and the point (0,3)

y=-3/4(x)

500

Convert to point-slope: -x+y=2, and the point (1,3).

y-3=x-1

Word Problems

100

A store sells gift cards in preset amounts. You can purchase gift cards for $10 or $25. You have spent $285 on gift cards. Write an equation in standard form to represent the situation. What are three combinations of gift cards you could have purchased?

10x+25y=285

11 $25, 1 $10; 9 $25, 6 $10; 7 $25, 11 $10; more possible.

200

You are preparing a fruit salad. You want the total carbohydrates from pineapple and watermelon to equal 24g. Pineapple has 3g of carbohydrates per ounce and watermelon has 2g of carbohydrates per ounce. Write an equation in standard form and list two possible solutions.

x=pineapple

y=watermelon

3x+2y=24

0 pineapple, 12 watermelon; 8 pineapple, 0 watermelon; 6 pineapple, 3 watermelon

300

Suppose your school is having a talent show to raise money. You think that 200 students and 150 adults will attend. It will cost $200 to put on the talent show. What is an equation that describes the ticket prices you can set for students and adults to earn $1000?

x=students

y=adults

200x+150y=1200

$6 students, free adults; free students, $8 adults; $3 students, $4 adults

400

A media download store sells songs for $1 and movies for $12. You have $60 to spend. Write an equation and list three possible solutions.

x=songs

y=movies

x+12y=60

0 songs, 5 movies; 60 songs, 0 movies; 12 songs, 4 movies

500

A store sells T-shirts for $12 each and sweatshirts for $15 each. You have $120 to spend. Write an equation and list three possible solutions.

x=shirts

y=sweatshirts

12x+15y=120

10 shirts, 0 sweatshirts; 0 shirts, 8 sweatshirts; 5 shirts, 4 sweatshirts

X- and Y- intercepts

100

Find the x and y intercepts of x+y=9.

(9,0)

(0,9)

200

Find the x and y intercepts of: x-2y=2.

(2,0)

(0,-1)

300

Find the x and y intercepts of: -3x+3y=7.

(-3/7,0)

(0,3/7)

400

Find the x and y intercepts of: 3x-5y=-20.

(-20/3,0)

(0,4)

500

Find the x and y intercepts of: 7x-y=21

(3,0)

(0,-21)

Slopes

100

Find the slope of: x+y=9.

-1

200

Find the slope of x-2y=2.

-1/2

300

Find the slope of -3x+3y=7.

1/7

400

Find the slope of 3x-5y=-20.

3/5

500

Find the slope of 7x-y=21.

-7