$$y = 3 \times 5 + 16 = 31$$ feet

$$y = 3 \times 10 + 16 = 46$$ feet

Question 1

What is the slope of the line represented by the equation $$y = 3x + 16$$?

Accepted Answer

$$3$$

Question 2

What does the y-intercept of the equation $$y = 3x + 16$$ represent in the context of the movable bridge?

Accepted Answer

The initial height of the bridge before it starts rising

Question 3

If the bridge rises for 5 seconds, what will its height be according to the equation $$y = 3x + 16$$?

Accepted Answer

$$y = 3 	imes 5 + 16 = 31$$ feet

Question 4

Which of the following best describes the graph of $$y = 3x + 16$$?

Accepted Answer

A straight line with positive slope

Question 5

How many feet does the bridge rise each second?

Accepted Answer

$$3$$ feet

Question 6

If the bridge starts at a height of 16 feet, how long will it take to reach a height of 40 feet?

Accepted Answer

$$x = \frac{40 - 16}{3} = 8$$ seconds

Question 7

Which real-world scenario could be modeled by the equation $$y = 3x + 16$$?

Accepted Answer

A savings account earning $$3 per month starting with 16$$

Question 8

If the bridge rises for $$x$$ seconds and reaches a height of $$y$$ feet, which equation would you use to solve for $$x$$?

Accepted Answer

$$x = \frac{y - 16}{3}$$

Question 9

What is the domain of the function $$y = 3x + 16 in $$the context of the bridge rising?

Accepted Answer

All non-negative real numbers

Question 10

If the bridge rises for 0 seconds, what is its height?

Accepted Answer

$$y = 16$$ feet

Question 11

Which of the following points lies on the graph of $$y = 3x + 16$$?

Accepted Answer

$$(2, 22)$$

Question 12

If the bridge rises for 10 seconds, what is its height?

Accepted Answer

$$y = 3 	imes 10 + 16 = 46$$ feet

Question 13

What is the range of the function $$y = 3x + 16$$ for $$x \geq 0$$?

Accepted Answer

$$y \geq 16$$

Question 14

If the bridge rises at a rate of 3 feet per second, what would the equation be if it started at 20 feet instead of 16 feet?

Accepted Answer

$$y = 3x + 20$$

Question 15

If the bridge needs to reach a height of 25 feet, how many seconds will it take?

Accepted Answer

$$x = \frac{25 - 16}{3} = 3$$ seconds

Question 16

Which of the following statements is true about the function $$y = 3x + 16$$?

Accepted Answer

The function is linear and increases as $$x$$ increases

Graphing a Linear Equation: Movable Bridge Height

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