Question

Write the general form of the equation of line ax + by + c = 0. In slope y intercept form y = mx + C

Answer 1

Hint:First we will take all the terms except y in the right hand side of ax + by + c = 0, then we will divide both the sides by b to convert it in the form of y = mx + C and then we will find the value of m and C .

Complete step-by-step answer:
Let’s start solving the question,
We have ax + by + c = 0,
Now we will take ax and c to the opposite side of the equation,
We get, by = -ax – c
Now we will divide both the sides of the equation by b.
Therefore we get,
$\begin{aligned} & \dfrac{by}{b}=\dfrac{-ax-c}{b} \\\ & y=\dfrac{-ax}{b}-\dfrac{c}{b} \\\ \end{aligned}$
Now by comparing it with y = mx + C we get,
$m=\dfrac{-a}{b},C=\dfrac{-c}{b}$
Hence, we have converted the given equation in y = mx + C form.

Note: We have used simple addition and division to convert ax + by + c = 0 in the form of y = mx + C, where m = slope and C = y intercept. One can try to convert y = mx + C in the form of ax + by + c = 0 and then check that the values that we have found for m and C are true or not.