Chapter 1.5, Problem 5E

Solution

a.

To find : The points determined by $-3,-2,-1,0,1,2,3$ ,where

  $x=2t,y=3t-1$

$t$	$x=2t$	$y=3t-1$	$\left(x,y\right)$
$-3$	$-6$	$-10$	$\left(-6,-10\right)$
$-2$	$-4$	$-7$	$\left(-4,-7\right)$
$-1$	$-2$	$-4$	$\left(-2,-4\right)$
$0$	$0$	$-1$	$\left(0,-1\right)$
$1$	$2$	$2$	$\left(2,2\right)$
$2$	$4$	$5$	$\left(4,5\right)$
$3$	$6$	$8$	$\left(6,8\right)$

Given information:

The given points are $-3,-2,-1,0,1,2,3$ and $x=2t,y=3t-1$

Concept used:

By substitution method can find the values of $t$ for $x\text{and }y$ .

Calculations:

Substitute each value of $t$ for $x\text{and }y$:

$t$	$x=2t$	$y=3t-1$	$\left(x,y\right)$
$-3$	$-6$	$-10$	$\left(-6,-10\right)$
$-2$	$-4$	$-7$	$\left(-4,-7\right)$
$-1$	$-2$	$-4$	$\left(-2,-4\right)$
$0$	$0$	$-1$	$\left(0,-1\right)$
$1$	$2$	$2$	$\left(2,2\right)$
$2$	$4$	$5$	$\left(4,5\right)$
$3$	$6$	$8$	$\left(6,8\right)$

This is the table of value $t$ for the for $x\text{and }y$.

b.

To find : The direct algebraic relation between $x\text{and}y$ , where

  $x=2t,y=3t-1$ .

The relation between $x\text{and}y\text{is}y=\frac{3x}{2}-1.$

Given information:

The given $x=2t,y=3t-1$ .

Concept used :

By using the substitution, method can find the relation.

Calculations:

Here

  $\begin{array}{l}x=2t\\ t=\frac{x}{2}\end{array}$

Substitute $t$ into the equation of $y$ .

  $\begin{array}{c}y=3\times \frac{x}{2}-1\\ =\frac{3x}{2}-1\end{array}$

So the relation between $x\text{and}y\text{is}y=\frac{3x}{2}-1.$

c.

To plot:The relation between $x\text{and}y\text{is}y=\frac{3x}{2}-1.$

Given information:

The given equation is $y=\frac{3x}{2}-1$ .

Plot the graph:

Graph the relation $y=\frac{3x}{2}-1$ cis given below.