Question

How do you write $6x-2y=9$ into slope intercept form?

Answer 1

Hint: Now we know that the slope intercept form a linear equation in two variables is given by $y=mx+c$ where m is the slope of the line and c is the intercept of the line. Now rearranging the terms of the given equation we will write the equation in the slope intercept form.

Complete step-by-step solution:
Now we are given with a linear equation in two variables. We know that such equations represent a straight line in the XY plane. Now we want to write the equation in slope intercept form.
Let us first understand the meaning of slope and intercept.
Slope of a line is the ratio of $\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$ for any two points $\left( {{x}_{2}},{{y}_{2}} \right)$ on the line. It is the value of $\tan \theta $ where $\theta $ is the angle made by line and x axis.
Similarly intercept is the y intercept of the line. It is the intersection of the line and y axis.
Now the equation in slope intercept form is written as $y=mx+c$ where m is the slope of the line and c is the intercept of the line.
Now consider the given equation $6x-2y=9$
Now transposing 6x on RHS we get the equation as,
$\Rightarrow -2y=9-6x$
Now dividing the whole equation by – 2 we get,
$\begin{align}
  & \Rightarrow y=-\dfrac{9}{2}+3x \\
 & \Rightarrow y=3x-\dfrac{9}{2} \\
\end{align}$
Now the above equation is in the form of $y=mx+c$ where $m=3$ and $c=\dfrac{-9}{2}$
Hence the given equation is in the slope intercept form.

Note: Now note that we also find the value of intercept of the line by substituting x = 0 in the equation. For example if we substitute x = 0 in the given equation then we get $-2y=9$ on rearranging we get $y=\dfrac{-9}{2}$ Hence $\left( 0,\dfrac{-9}{2} \right)$ is the point on the line and hence is the y intercept of the line.