Model Linear Equations

Starting at sunrise, the temperature rose 2.5⁰ every hour. After 8 hours, the temperature was 67⁰. Write an equation in point-slope form to model the temperature, y, after x hours after sunrise. If sunrise was at 6:00 AM, what is the temperature at noon?

•   y+67=2.5(x+8) ; the temperature was 62⁰ at noon

•  y−67=2.5(x−8); the temperature was 62⁰ at noon

•  y−67=2.5(x−8); the temperature was 77⁰ at noon

•  y−8=2.5(x−67); the temperature was 77⁰ at noon

The aquarium is draining a large fish tank. The pump they are using can drain 24 gallons per hour. After 3 hours, there are 78 gallons left in the tank. Write an equation in slope-intercept form to model the water left in the tank, y, after x hours of draining. How many gallons were originally in the tank?

Allie orders candles from an online company that offers flat rate shipping. She placed an order for 4 candles for $35. A few months later, she placed an order for 12 candles for $95. Write an equation in point-slope form to model the total cost, y, for ordering x candles. How much is shipping?

Which equations form a linear function?

Which equation represents the graph of the function with point (-2, 5) and slope of 3?

What is the equation and slope of the line shown on the grid?

• y = 6; slope is -1

• x = 6; slope is zero

• y = 6; slope is 6

• x = 6; slope is undefined

Which equation represents y = -3x + 5 in point-slope form?

At the beginning of the summer, Jenna had saved $141.  To earn money of the summer, she is working part time at the local community center.  She will earn $32 per day of work.  If x represents the number of days she works, which of the following equations represents how much money she will have, including her savings?

• y = 141-32x

• y = x + 141

• y = 32x + 141

• y = 141x + 32

A strong cold front blew through during the night.  The temperature outside began to drop rapidly.  The graph shows the temperature at each hour after the cold front blew through.  What is the rate of change of the graph?

• 2.5°F per hour

• 0.2°F per hour

• -0.2°F per hour

• -2.5°F per hour

Stephanie planted a home garden.  She planted 2 rows of tomatoes with 4 tomato plants in each row.  She also planted squash in rows of 6 plants each.  If x represents the number of rows of squash she planted, which of the following equations can be used to find the total number of plants Stephanie planted in her home garden?

• y = 6x + 6

• y = 8x + 6

• y = 7x + 6

• y = 6x + 8