Question

How do you express the following equation in slope intercept form $7x-5y=10$?

Answer 1

Hint: Try converting the equation to slope intercept form first i.e. $y=mx+c$. This can be done by performing arithmetic operations on both sides of the equation. Keeping ‘y’ on the left side of the equation try to bring the whole equation to $y=mx+c$ form.

Complete step-by-step solution:
Slope intercept form: We have the slope intercept form of a linear equation as $y=mx+c$, where ‘m’ represents the slope and ‘c’ is the y-intercept.
Converting the equation to slope intercept form means we have to bring the equation in $y=mx+c$ form.
Now let’s consider our equation $7x-5y=10$
To keep ‘y’ on the left side of the equation it can be written as
$\Rightarrow -5y=10-7x$
Which can also be written as
$\Rightarrow -5y=-7x+10$
Dividing both sides by $-5$, we get
$\Rightarrow \dfrac{-5y}{-5}=\dfrac{-7x+10}{-5}$
After cancelling out $-5$ both from numerator and denominator on the left side of the equation, we get
$\Rightarrow y=\dfrac{-7x+10}{-5}$
Separating the division on the right side of the equation, we get
$\Rightarrow y=\dfrac{-7x}{-5}+\dfrac{10}{-5}$
It can be simplified as
$\begin{align}
  & \Rightarrow y=\dfrac{7x}{5}+\left( -2 \right) \\
 & \Rightarrow y=\dfrac{7x}{5}-2 \\
\end{align}$
This is the required slope intercept form for the given equation.

Note: The equation must be brought to $y=mx+c$ form. ‘y’ should be kept fixed on the left side to perform necessary arithmetic operations for converting the whole equation to slope intercept form. After converting the the equation the value of ‘y’ which we got $y=\dfrac{7x}{5}-2$, can be compared to $y=mx+c$; from which we can get $m=\dfrac{7}{5}$ and $c=-2$.