Problem Statement
We are asked to find the y-intercept of the following equation:
[tex]y=3x-4[/tex]
Method
To solve this question, we simply look at the general slope-intercept form of the equation of a line which is given as:
[tex]\begin{gathered} y=mx+c \\ \text{where,} \\ m=\text{slope} \\ c=\text{ y-intercept} \end{gathered}[/tex]
Now, all we need to do is to compare the general form given above to the equation given in the question to find the y-intercept of the equation.
Solution
Comparing the general slope-intercept form with the equation of the line as follows:
[tex]\begin{gathered} y=3x-4 \\ y=mx+c \\ \\ \text{This implies that:} \\ 3x=mx \\ \text{Divide both sides by }x \\ \frac{mx}{x}=\frac{3x}{x} \\ \\ \therefore m=3 \\ \\ c=-4 \end{gathered}[/tex]
Thus, the y-intercept is -4
Final Answer
The y-intercept is -4
