Question

How do you convert $4x + 3y - 8 = 0$ into slope intercept form?

Answer 1

We will first of all take all the terms except the term with $y$ from left hand side to the right hand side, then we will just divide the equation by 3 and have the required answer.

Complete step by step solution:
We are given that we are required to convert $4x + 3y - 8 = 0$ into slope intercept form.
We will first take 4x from addition in the left hand side to subtraction in the right hand side, we will then obtain the following expression with us:-
$\Rightarrow 3y - 8 = - 4x$
Now, we will just take 8 from subtraction in the left hand side to addition in the right hand side, we will then obtain the following expression with us:-
$\Rightarrow 3y = - 4x + 8$
Taking 3 from multiplication in the left hand side to division in the right hand side, we will then obtain the following equation with us:-
$\Rightarrow 3y = \dfrac{{ - 4x + 8}}{3}$
The above mentioned equation can also be written as follows:
$\Rightarrow y = - \dfrac{4}{3}x + \dfrac{8}{3}$

Thus, we have the required answer as $y = - \dfrac{4}{3}x + \dfrac{8}{3}$.

Note:
The students must note that the slope – intercept of a line is given by y = mx + c, where m is the slope of the line and c is the y - intercept.
Now, the equation we found is $y = - \dfrac{4}{3}x + \dfrac{8}{3}$, therefore, the slope of the given line is $- \dfrac{4}{3}$ and the y – intercept of this line is given by $\dfrac{8}{3}$.
The students must also know that the slope is tangent of the angle which the line makes with the positive – x axis. Here, it means that the tangent of the angle line given to us which is $4x + 3y - 8 = 0$ makes with the positive direction of x – axis is $- \dfrac{4}{3}$.
The students must also note that we convert the equation in slope – intercept form so that it is easy to find the slope and the intercepts of the given line.