Question

Aria is paddling a canoe at a constant speed. She starts a timer when she is 40 feet from her starting position. After 30 seconds, Aria is 130 feet from her starting position. Write a linear equation in slope-intercept form to find the distance d of Aria from her starting position after t second.

Answer 1

Answer:

$y = 3x + 40$

Step-by-step explanation:

The slope-intercept equation takes the form

$y = mx + c$

Where m is the gradient, and c is the y-intercept.

If we assume we are plotting a graph where the X axis is time, and the y axis is distance, and we know our time value starts at 40, then we can say that our y intercept value is 40.

Next, let's figure out how far she has travelled. 130-40 = 90, and she has travelled this distance in 30 seconds, so dividing 90 by 30, we know that she is travelling 3 feet a second. This leaves us with a gradient of 3.

Putting these two values together, we can find the final form of the equation to be:

$y = 3x + 40$

Answer 2

Answer:

d = 3t + 40

Step-by-step explanation:

So, since you have a constant speed you're going to have a linear equation, which was also stated in the question. So it's asking for slope-intercept form which is expressed as: y=mx+b, where m=slope, and b=y-intercept. So it's important to know what these two things mean in certain contexts. In every single case, the slope is how much the y-value is changing as x increases by 1, and in this specific case, the distance is what is changing as time goes by. So this means that the distance would be the y-value, and x would be the t variable (time). And remember how it mentioned "constant speed", this means as one second passes, the distance increases by a constant distance. We can solve for this by using the given information.

She's already 40 feet from her starting position, and after 30 seconds she's 130 feet from her starting position. This means she traveled (130 - 40) feet, because she was already 40 feet away from her starting position. This means she traveled 90 feet. Now to find how much she travels in a second, divide it by the time which is 30 seconds, and you get: 90 feet / 30 seconds = 3 ft/s, this is her constant speed. This is the slope of the equation. So now we have the equation: d = 3t + b. Now all we need to find is the y-intercept

The y-intercept in this context, is how far away she is from her starting position initially. This is given in the problem, it's 40 feet. She's already 40 feet away when 0 seconds have passed. So this gives us the equation: d = 3t + 40