Question

Aidan and his sister Ella are having a race. Aidan runs at a rate of 10 feet per second. Ella runs at a rate of 6 feet per second. Since Ella is younger, Aidan is letting her begin 30 feet ahead of the starting line.

Let y represent the distance from the starting line and x represent the time elapsed, in seconds. Write an equation to model the distance Aidan traveled. Write an equation to model the distance Ella traveled.

Answer 1

Aidan: y = 10x

Ella: y = 6x+30

Step-by-step explanation:

By using the formula for linear equation y = mx + b and distance = speed x time, we are able to create a linear equation for both Aidan and Ella.

Ella has a head start of 30 ft while running at 6 ft/s. So 30 is the y - intercept since she didn't start at 0. 6 ft/s is her running speed, which multiplies the time(that is unknown so we use "x") to get the distance.

Aidan did not have a head start which means he started at zero, which leads to his equation not having a y - intercept. 10 ft/s is his running speed, which multiplies the time to get the distance.

Answer 2

Answers:

• Aidan's equation is y = 10x
• Ella's equation is y = 6x+30

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Step-by-step explanation:

Aidan runs at 10 ft per sec. This is the rate of change aka slope. So we have m = 10 for Aidan.

He starts at the starting line, meaning he starts when y = 0. This is the y intercept. We have b = 0.

We'll then go from y = mx+b to y = 10x+0 or y = 10x to represent how far he is from the starting line after x seconds. For instance, if x = 5 seconds elapse, then he has traveled 50 feet (because 10x = 10*5 = 50).

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Ella's rate is 6 ft per sec, which means m = 6 is her slope.

She starts 30 feet ahead of the starting line. Ella's y intercept is b = 30.

We go from y = mx+b to y = 6x+30 to represent how far she is from the starting line after x seconds elapse.

Example: if x = 10 then she is y = 90 feet away from the starting line (because 6x+30 = 6*10+30 = 90).