Raj gets a 1.5 mile head start and runs at a rate of 4.5 miles per hour. jacinda's progress is represented by a graph that goes through the points (1,10), (2,20), and (3,30). how long will jacinda need to run to catch up with raj?

From the given ordered pair representing Jacinda's progress, her speed is equal to 10 miles per hour. Letting x be the time it takes for Jacinda to catch up with Raj, the total distance Raj would travel is 
                            1.5 + 4.5x
and Jacinda's total distance is 10x. Mathematically,
                                1.5 + 4.5x = 10x 
The value of x from the equation is 0.27 hours. Therefore, Jacinda needs to run 2.7 miles to catch up with Raj. 

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.