Suppose you graphed every single point of the form $(2t + 3, 3-3t)$. For example, when $t=2$, we have $2t + 3 = 7$ and $3-3t = -3$, so $(7,-3)$ is on the graph. Explain why the graph is a line, and find an equation whose graph is this line.

Guest Nov 23, 2017

#1**+2 **

This graphs a line because for every increase in t by 1, x changes by 2 and y changes by -3

We only need two points to find a line

If t = 0 we have the point (3,3)

If t = 1, we have the point (5,0)

The slope of this line is -3/2 [ just as we suspected !!!! ]

And using (5,0), the equation of the line is

y = (-3/2)(x - 5)

y = (-3/2)x + 15/2

To see that this is true.....when t = 2, x = 7 and y = -3

So

y = (-3/2)(7) + 15/2

y = -21/2 + 15/2

y = -6/2 = -3

CPhill
Nov 23, 2017