Question

How do you graph $y=\dfrac{1}{2}x-6$ ?

Answer 1

Hint: At first, we compare the given equation with the slope-intercept form of a straight line and find out the slope and y-intercept. Then we plot the point $\left( 0,-6 \right)$ and draw another line through this point making an angle ${{\tan }^{-1}}\left( \dfrac{1}{2} \right)$ with the $x$ -axis. This is the required line.

Complete step by step answer:
The general slope-intercept form of a straight line is
$y=mx+c$
Where, $m$ is the slope of the line and c is its $y$ -intercept.
And the given equation is
$y=\dfrac{1}{2}x-6$
First of all, we recognise that this is a linear equation, so it is an equation of a straight line. Comparing the given equation with that of the general slope-intercept form, we get
$m=\dfrac{1}{2}$ and $c=-6$
$y$ -intercept $6$ means that the point where the line intersects the $y$ -axis, is $\left( 0,-6 \right)$ . Therefore, we plot this point on the graph paper.
Slope of a line means the tangent of the angle that the line makes with the positive $x$ -axis. If we are given the slope, we can find the angle which the line makes by the equation,
$\theta ={{\tan }^{-1}}m$
We draw a line at $\left( 0,-6 \right)$ which will be parallel to $x$ -axis. The angle made by this line with the $x$ -axis then, will be
$\theta ={{\tan }^{-1}}\dfrac{1}{2}$
$\Rightarrow \theta ={{26.5}^{\circ }}$
Then, we draw another line at $\left( 0,-6 \right)$ which makes this $\theta $ angle with the parallel line previously drawn at this point.
Therefore, we can conclude that the last line that we have drawn is nothing but our required line.

Note:
Students must be careful while finding out the angle made by the line with the $x$ -axis. This problem can also be solved by taking any points that lie on the given line and plot them. Then, if we draw a line joining the points, we get our desired line.