Question

How do you find the slope of a given equation $4x-5y=3$?

Answer 1

To find the slope of the given equation $4x-5y=3$, we are going to use the general form of the equation of a straight line which is $y=mx+c$. We are comparing the given equation by equation of a straight line because the given equation is the equation of a straight line. Now, we are going to arrange the given equation in such a manner so that the coefficient of y becomes 1 and is written in this form:$y=mx+c$.In this form, “m” is the slope.

Complete answer:
The equation given in the above problem in which we have to find the slope is:
$4x-5y=3$ ……………. Eq. (1)
As you can see that the above equation is a straight line equation and we know that the general form of the equation of a straight line is:
$y=mx+c$………. Eq. (2)
In the above equation, “m” is the slope of the straight line so we are going to arrange the given equation in the above form.
Adding 5y on both the sides of eq. (1) we get,
$\begin{aligned} & 4x-5y+5y=3+5y \\\ & \Rightarrow 4x=3+5y \\\ \end{aligned}$
Subtracting 3 on both the sides we get,
$4x-3=5y$
Dividing 5 on both the sides we get,
$\begin{aligned} & \dfrac{4x-3}{5}=y \\\ & \Rightarrow \dfrac{4x}{5}-\dfrac{3}{5}=y \\\ \end{aligned}$
Now, interchanging the terms on both the sides we get,
$y=\dfrac{4x}{5}-\dfrac{3}{5}$
Comparing the above equation with eq. (2) we get,
$y=\dfrac{4x}{5}-\dfrac{3}{5}$
$y=mx+c$
From the above, the value of m in the given equation is $\dfrac{4}{5}$.
Hence, the slope of the given equation is equal to $\dfrac{4}{5}$.

Note:
Just like in this question, we have asked to find the slope of the given equation, In some other question, you might be asked to find the y intercept of the given equation.
The y intercept of the given equation is the constant “c” in the general form of a straight line which we have shown above:
$y=mx+c$
Now, comparing the above equation with this equation $y=\dfrac{4x}{5}-\dfrac{3}{5}$ which we have rearranged in the above solution we get,
$y=mx+c$
$y=\dfrac{4x}{5}-\dfrac{3}{5}$
On comparing the above two equations we get the value of “c” as:
$c=-\dfrac{3}{5}$
Hence, we got the y intercept of the given equation is $-\dfrac{3}{5}$.