# How do you find the range given x=3-2t and y=2+3t for -2 ≤ t ≤ 3?

Apr 23, 2018

$\left[- 2 , 8\right]$

#### Explanation:

the range is the difference between the least point and highest point from the $x$ axis

which are the $y$ values

$y = 2 + 3 t$

Substiutute

$t = - 2$ $\rightarrow \text{ }$$y = - 2$

$t = 3$ $\rightarrow \text{ }$$y = 8$

so your range will be $\left[- 2 , 8\right]$

Apr 23, 2018

Given: $y = 2 + 3 t \text{ [1]}$ and $- 2 \le t \le 3 \text{ [2]}$

Solve equation [1] for $t$ in terms of $y$:

$y = 2 + 3 t \text{ [1]}$

$3 t = y - 2$

$t = \frac{y - 2}{3} \text{ [1.1]}$

Substitute equation [1.1] into inequality [2]:

$- 2 \le \frac{y - 2}{3} \le 3$

Multiply the inequality by 3:

$- 6 \le y - 2 \le 9$

$- 4 \le y \le 11 \leftarrow$ this is the range.