Graph the parametric equation x = 2t y = t + 5, -2 ≤ t ≤ 3

Just fun I'm going to add something above the below.

You can write an equation for this without the parameter.

You have y=t+5 and x=2t.  If you multiply both sides of y=t+5 by 2 you should get 2y=2t+10 and guess what you can replace 2t with x since you have x=2t.  So you can write 2y=x+10 as your equation to represent the parametric version they have here.

This is a linear equation as our graph appears to be below.   Solve for y by dividing both sides by 2 gives you y=x/2  +5.  The slope is 1/2 and the y-intercept is 5.  If t is between -2 and 3 then x is between -4 and 6 since x is doubled t (inclusive here since we have those equal signs along with those inequalities).

So you could have just graph the line y=x/2+5 on the interval /

Anyways, I'm also going to look at this without the rewrite:

I'm going to make a table with 4 columns.  The first column is t.  The second is x(t), the third is y(t), and the fourth will be a list of points (x,y) our relation will go through).

t    |     x(t)        |     y(t)           |   (x,y)

------------------------------------------------------

-2       2(-2)=-4      -2+5=3          (-4,3)

-1        2(-1)=-2       -1+5=4           (-2,4)

0        2(0)=0         0+5=5           (0,5)

1         2(1)=2           1+5=6           (2,6)

2        2(2)=4          2+5=7          (4,7)

3        2(3)=6          3+5=8           (6,8)

Now I'm going to graph the points in the last column on a coordinate-plane.

The horizontal axis is your x-axis and the vertical axis is your y-axis. I did the x-axis going up or down by two's while the y-axis is going up and down only by one's.

i'm pretty sure it's 477,585,296, but perhaps my math is incorrect.

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).