Modeling Situations Using Linear Relationships

How can you write the equation for a linear function if you know only two ordered pairs for the function?

• Use the two ordered pairs to find the slope (m). Then substitute the slope and one set of ordered pairs into y=mx+b to solve for b.

• Use the two ordered pairs to find the y-intercept (b). Then substitute the y-intercept and one set of ordered pairs into y=mx+b to solve for m.

• Use the two ordered pairs to find the value of y. Then substitute the the value of y and one set of ordered pairs into y=mx+b to solve for x.

• Use the two ordered pairs to find the value of x. Then substitute the the value of x and one set of ordered pairs into y=mx+b to solve for y.

A line passes through the points (5, –7.5) and has a y-intercept 10.

Which is a linear function in the form of y = mx + b for this line?

• y = 0.5x + 10

• y = –1.5x + 10

• y = –3.5x + 10

• y = 10x – 3.5

Write a function in the form y=mx+b for the line that passes through the points (2,4) and (6,16)

• y = 3x - 2

• y = 2x + 4

• y = 6x + 16

• y = 2x + 6

Max puts a stopper in the bathtub and turns on the faucet at t = 0.

After 5 minutes, there are 11 gallons of water in the tub and after 10 minutes, there are 22 gallons in the tub.

Write an equation that relates the number of gallons, g, to the time, t.

Does the relationship represent a linear function? Justify your response.

• g = 2.2t; The equation represents a linear function because the equation is in the form y = mx.

• g = 2.2t; The equation does not represent a linear function because the equation is not in the form y = mx + b.

• g = 4.4t; The equation represents a linear function because the equation is in the form y = mx.

• g = 4.4t; The equation does not represent a linear function because the equation is not in the form y = mx + b.

Sierra is building a skateboard ramp.

She wants the ramp to have a height, h, of 15 inches and a base length, l, of 54 inches.

Which linear function models the situation?

• y = (5/18)x

• y = (18/5)x

• y = 5x + 18

• y = 18x + 5

What is the equation for this line?

• y = x - 2
• y = x + 2
• y = 2x
• y = -x + 2

Find the slope given the following points: (5,1) and (3,1)

• m=1/4
• m=0
• m=1
• m=undefined

Lee charges $3 for a basket and $2.50 for each pound of fruit picked at the orchard. Write an equation in y = mx + b form for the total cost of x pounds of fruit from the orchard.

• y = 3x + 2.5
• y = 2.50x + 3
• y = 2.50x 
• y = 3x + 2.50

Which equation matches the table?

• y = x + 5
• y = 5x
• y = x - 5
• x = y - 5

Bowling costs $4 for shoe rental plus $5 for every game. Which equation shows how much it costs to go bowling for x games?

• y = 4 + 5x
• y = 5 + 4x
• y = 4•5•x
• y = 5x - 4