graphical models

Question

1. a) Explain how you know which of the graphs below represent a linear relation or quadratic relation. Consider the description for the path of each graph in your explanation as well. 

b) Determine the equation for the linear relation. Show all your work on how you got the key features from the graph for the equation. 

c) Graphically (show your work on the graph) and algebraically (use the equation to show your work) determine the amount of gallons in the tank for 90 miles driven. 

d) Graphically (show your work on the graph) and algebraically (use the equation to show your work) determine the miles driven for 9.5 gallons of tank.

Answer 1

Linear equations make graphs that are straight lines.

Quadratic equations make graphs that are parabolas - hills or valleys.

Answer 2

(a) if the change in y is constant per unit change in x, then it is linear, otherwise quadratic. So first is linear and second quadratic.

(b) y = mx + b. (0,b) is the y intercept so b = 15.

m = slope. Line goes through (25,14) and (50,13) so slope = [ 13-14] / [50-25] = -1/25

So y = (-1/25) x + 15

(c) Read y from the graph when x = 90.

Substitute x = 90 into the equation from (b)

(d) Read x from the graph when y = 9.5

Find x when 9.5 = (-1/25)x + 15