Chapter 1.2, Problem 15E

To determine

Complete the table given below for the equation $y=-2x+5$ and use the resulting solution points to sketch the graph of the equation.

$x$	$-1$	$0$	$1$	$2$	$\frac{5}{2}$
$y$
$\left(x,y\right)$

Answer to Problem 15E

The table is

$x$	$-1$	$0$	$1$	$2$	$\frac{5}{2}$
$y$	$7$	$5$	$3$	$1$	$0$
$\left(x,y\right)$	$\left(-1,7\right)$	$\left(0,5\right)$	$\left(1,3\right)$	$\left(2,1\right)$	$\left(\frac{5}{2},0\right)$

The graph of the equation is:

  

Explanation of Solution

Given:

The equation $y=-2x+5$ and table to fill

$x$	$-1$	$0$	$1$	$2$	$\frac{5}{2}$
$y$
$\left(x,y\right)$

Concept Used:

The graph of an equation is the smooth curve of all the points satisfying the equation.

Calculation:

For the givenequation $y=-2x+5$

At $x=-1$

  $\begin{array}{c}y=-2\left(-1\right)+5\\ =2+5\\ =7\end{array}$

At $x=0$

  $\begin{array}{c}y=-2\left(0\right)+5\\ =0+5\\ =5\end{array}$

At $x=1$

  $\begin{array}{c}y=-2\left(1\right)+5\\ =-2+5\\ =3\end{array}$

At $x=2$

  $\begin{array}{c}y=-2\left(2\right)+5\\ =-4+5\\ =1\end{array}$

At $x=\frac{5}{2}$

  $\begin{array}{c}y=-2\left(\frac{5}{2}\right)+5\\ =-5+5\\ =0\end{array}$

The table is

$x$	$-1$	$0$	$1$	$2$	$\frac{5}{2}$
$y$	$7$	$5$	$3$	$1$	$0$
$\left(x,y\right)$	$\left(-1,7\right)$	$\left(0,5\right)$	$\left(1,3\right)$	$\left(2,1\right)$	$\left(\frac{5}{2},0\right)$

Joining the points and plotting the graph, we have

  

Conclusion:

The table is

$x$	$-1$	$0$	$1$	$2$	$\frac{5}{2}$
$y$	$7$	$5$	$3$	$1$	$0$
$\left(x,y\right)$	$\left(-1,7\right)$	$\left(0,5\right)$	$\left(1,3\right)$	$\left(2,1\right)$	$\left(\frac{5}{2},0\right)$

The graph of the equation is: