Let C be the curve parametrically defined by the equations x$($t$)=$ t$31$ and y$($t$)=15$t$.$

$($a$)$ Create a table of values to sketch a plot of this curve on the interval $3$ t $3.$ Draw arrows on

your graph to indicate the direction of positive orientation.

$($b$)$ Find an expression for the slope dy

dx of the curve in terms of t and use it to find the equation of the

line tangent to C where it crosses the y$-$axis. Add this line on your graph from $($a$).$

$($c$)$ Eliminate the parameter t and express the set of points as a function, either x $=$ h$($y$)$ or y $=$ h$($x$)$

$($you decide which is easier$$there are multiple valid answers$)$