The following questions will provide practice working with simple linear functions. All questions refer to a coordinate graph with the variable \(X\) on the horizontal axis and the variable \(Y\) on the vertical axis.

a. If two points on a straight line are \((X=3, Y=2)\) and \((X=12, Y=5)\), what is the slope of the line?

b. If point \(A\) is at \((X=20, Y=20)\) and point \(B\) is at \((X=10, Y=40)\), what is the slope of the straight line joining points \(A\) and \(B\) ?

c. What is the slope of the function described by \(Y=12000-0.5 X\) ?

d. What is the slope of a line described by \(Y=6.5 X\) ?

e. What is the slope of a line described by \(Y=27+\) \(3.2 X\) ?

f. What is the \(Y\)-intercept of the function \(Y=1000\) \(+m X\) ?

g. What is the \(Y\)-intercept of the function \(Y=-100\) \(+10 X\) ?

h. What is the \(X\)-intercept of the function \(Y=10-\) \(0.1 X\) ?

i. Suppose ABC Corp. spends \(\$ 100 000\) per year on some basic level of advertising, regardless of its revenues. In addition, the company spends 15 percent of each dollar of revenue on extra advertising. Write a mathematical equation that describes the functional relation between advertising \((A)\) and revenue \((R)\).