Consider that we and our friend begin to run along a path at different constant speeds. After 1 minute our friend is 45 meters ahead of us and after 3 minutes, 105 meters in front of us. We want to write an equation for the distance y our friend is ahead of us after x minutes. To do so, let's rewrite the given information as ordered pairs.
(Distance,Time) → (1,45) and (3,105)
Here, (1,45) represents the distance after 1 minute and (3,105) represents the distance after 3 minutes. Now, remember that equations written in point-slope form follow a specific format.
y- y_1= m(x- x_1)
In this form, m is the slope of the line and ( x_1, y_1) is a point on the line. We will determine the slope with the slope formula and using the obtained ordered pairs.
Now that we know the slope is 30, we can write the equation of the line in point-slope form. We can use either of the obtained points as (x_1,y_1) in our equation. Let's use ( 1, 45).
To graph this function, let's plot the ordered points in a coordinate plane and connect them with a line.
We want to know if we started from the same spot as our friend. To do so, let's recall the equation obtained in Part A.
y=30x+15
Consider that the initial time is x=0. Let's substitute this value into the above equation!
