a) The amount of money that Tanisha spent to buy the car is $20,000.
b) The rate of change of Tanisha's car over time -2000 per year.
c) A possible equation to represent the relationship between the value of Peter's car and time is V = -2000t + 20,000.
In Mathematics and Geometry, the slope-intercept form of the equation of a straight line refers to the general equation of a linear function and it is represented by this mathematical equation;
y = mx + b
Where:
- m represents the slope or rate of change.
- x and y are the points.
- b represents the y-intercept or initial value.
Part a.
The amount of money that Tanisha spent to buy the car is represented by the y-intercept of the graph, which is equal to $20,000.
Part b.
The rate of change Tanisha/s over time can be calculated as follows;
Rate of change = rise/run
Rate of change = -1200/6
Rate of change = -2000 per year.
Part c.
Since Peter's car costs less than Tavisha's, but the value of both cars changes at the same rate, a possible equation to represent the relationship between the value of Peter's car (V) in dollars, and time (t) in years, can be written as follows;
V = mt + b
V = -2000t + 20,000.