Question

How do you graph the equation $y = x + 5$?

Answer 1

Hint: The given equation is an equation of straight line. To graph $y = x + 5$ using slope and $y$-intercept, we must know the general equation of straight line. The general equation of straight line is $y = mx + c$ where $m$ is the slope and $c$ is $y$-intercept. By comparing the given equation with $y = mx + c$, we can find the values of $m$ and $c$. Using these values, we will draw the graph of the given equation.

Complete step-by-step answer:
Here the given equation is $y = x + 5 \cdots \cdots \left( 1 \right)$. We know that the general equation of the straight line is given by $y = mx + c \cdots \cdots \left( 2 \right)$ where $m$ is the slope and $c$ is $y$-intercept. The equation $\left( 2 \right)$ is also called slope-intercept form of straight line.
Let us compare the equation $\left( 1 \right)$ with the equation $\left( 2 \right)$. So, we can write the slope is $m = 1$ (coefficient of $x$) and $y$-intercept is $c = 5$. Note that here $y$-intercept is $c = 5$ so we can say that the straight line is passing through the point $\left( {0,5} \right)$. Also note that here slope is $m = 1$ so we can say that if there is change of one unit in $x$ then there will be change of one unit in $y$.
Let us find $x$-intercept by putting $y = 0$ in the equation $\left( 1 \right)$. Hence, we get $x = - 5$. Note that here $x$-intercept is $ - 5$ so we can say that the straight line is passing through the point $\left( { - 5,0} \right)$.
Now we have the following information:
$\left( 1 \right)$ The required straight line is passing through the points $\left( { - 5,0} \right)$ and $\left( {0,5} \right)$.
$\left( 2 \right)$ The slope of the required line is $m = 1$.
As per the above information, we can draw the graph of the given equation in the following manner.

Note:
Rewrite the given equation as $x = y - 5$ and compare with the general equation$x = my + c$, we get $m = 1$ and $c = - 5$. Here $m = 1$ is slope and $c = - 5$ is $x$-intercept. To obtain $x$-intercept, we have to put $y = 0$ in the given equation. To obtain $y$-intercept, we have to put $x = 0$ in the given equation. To graph $y = x + 5$, we can use another method in which first we will find points by putting different values of $x$. Then, by joining all those points we can get the graph of the given equation.