Question

How do you write an equation with slope 3 and y – intercept as – 4?

Answer 1

Hint: We will first write the general equation of a line, then we will put the slope in that as given and then put x = 0 and find the y – intercept and equate it to – 4.

Complete step-by-step solution:
We are given that we need to write an equation with slope 3 and y – intercept as – 4.
We know that the general equation of a line is given by y = mx + c, where m is the slope of the line.
Since, we are given that the slope is 3.
Therefore, let us put m = 3 in the general equation, so we will obtain the following equation with us:-
$ \Rightarrow $y = 3x + c
Now, we know that the y – intercept is found when x = 0.
Putting x = 0, we will then obtain the following equation with us:-
$ \Rightarrow $y = c
Since we are already given that the y – intercept is – 4.
Comparing both, we will then obtain the following expression with us:-
$ \Rightarrow $c = - 4
Thus, putting this as well, we will then obtain the following equation with us:-
$ \Rightarrow $y = 3x – 4

Hence, the required answer is y = 3x – 4.

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.