Chapter 4.5, Problem 39MR

To determine

To graph: The equation by making table and connecting point to make a straight line.

Answer to Problem 39MR

The graph is straight line.

Explanation of Solution

Given:

  $y=x+1.5$ .

Concept used:

The graph of the function $\text{f}$ is the set of all point in the plane of the form $\left(\text{x,f}\left(\text{x}\right)\right)$ .

The graph can be defined by the graph of $\text{f}$ and the equation for the graph will be $\text{y=f}\left(\text{x}\right)$ .

The graph of the function is special case of the graph of an equation.

Domain $x$ is independent variable and range $y$ is dependent variable.

By connecting all point made that satisfy the equation the straight line can be graph.

Calculation:

Consider the equation:

  $y=x+\mathrm{1.5......}\left(i\right)$ .

The function rule represents $y$ as a linear function of $x$ . Observe that the domain of the function is set of all real numbers choose few negative and few positive values of the independent variable $x$ and then use the function rule to get the corresponding values of the dependent variable $y$ .

Domain $=\left\{x:x\in R\right\}$ .

Range $=\left\{y:y\in R\right\}$ .

Step $1$ : first find the ordered pairs for some selected values of $x$ within the domain. Since, the domain is the set of all real numbers choose few negative and few positive value of the independent variable $x$ and then use the function rule to get the corresponding values of the dependent variable $y$ . Use the value to prepare the table.

Table:

$x$	$-5$	$-4$	$-3$	$-2$	$-1$	$0$	$1$	$2.5$	$5$
$y$	$-3.5$	$-2.5$	$-1.5$	$-0.5$	$0.5$	$1.5$	$2.5$	$4$	$6.5$

Step $2$

: plot these ordered pairs as points in the coordinate plane and join them to draw the graph.

The graph is a straight line.

Hence, the graph is straight line.