Question

How do you write 3x = - 2y + 4 in slope – intercept form?

Answer 1

Hint: We will first write the general slope – intercept form and then compare it with the given form. Then, we will have the required slope – intercept form.

Complete step-by-step solution:
We are given that we are required to write the equation 3x = - 2y + 4 in the slope – intercept form.
We know that the general equation of a line in the slope – intercept form is given by: y = mx + c, where m is the slope of the given line.
Now, since we are given the line as: 3x = - 2y + 4
Taking the 2y from subtraction in the right hand side to addition in the left hand side, we will then obtain the following equation with us:-
$ \Rightarrow $ 3x + 2y = 4
Taking the 3x from addition in the left hand side to subtraction in right hand side, we will then obtain the following equation with us:-
$ \Rightarrow $ 2y = 4 – 3x
Dividing both the sides of the equation in the above line, we will then obtain the following equation with us:-
$ \Rightarrow y = \dfrac{{4 - 3x}}{2}$
Simplifying it, we will then obtain the following equation with us:-
$ \Rightarrow y = - \dfrac{3}{2}x + 2$

Therefore $y = - \dfrac{3}{2}x + 2$ is the required answer.

Note: The students must note that the x and y intercepts basically refer to the points where the line cuts the x – axis and y – axis at. The point where coordinate axis cut the line at x – axis is x – intercept and y – axis is y – intercept.
The students must also know that the slope of a line is basically the tangent of the angle the line makes with the positive x – axis. Here, in this question, we have tangent of the angle the given line is making with the positive x – axis as 1.