Question

How do you find the slope and intercept of $4x-y=13$?

Answer 1

As the general equation of a straight line is given as $y=mx+c$where, m is the slope and c is the intercept. This form is also known as the slope intercept form of an equation. By using this concept we will find the values of slope and intercept of $4x-y=13$.

Complete step by step answer:
We have been given an equation $4x-y=13$.
We have to find the slope and intercept of the given equation.
We know that the standard form of the equation of a straight line is given as $y=mx+c$.
Here m is the slope of the straight line and c is the y-intercept.
Now, we can write the given equation as
$\begin{aligned} & \Rightarrow 4x-13=y \\\ & \Rightarrow y=4x-13 \\\ \end{aligned}$
Which is of the form $y=mx+c$.
Now, by comparing the coefficients of the line we will get
$\Rightarrow m=4$ and $\Rightarrow c=-13$

So we get the slope and y-intercept of the line $4x-y=13$ as $m=4\text{ and }c=-13$ respectively.

Note: If the general equation of the line is of the form $ax+by+c=0$ then the slope of the line is given by $\dfrac{-a}{b}$ and the y-intercept is given by $\dfrac{-c}{a}$. Also if the value of y-intercept is equal to zero then the line is passing through the origin. The slope of the line will be either positive or negative. We can also find the slope of the line by equating the first order derivative of the equation equal to zero and put x=0 to find the value of y-intercept.