# How do you graph the equation y=4x-2?

May 20, 2017

The general equation for a line is $y = m x + b$, where:

• $y$ is the dependent variable (dependent on $x$).
• $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$ is the slope.
• $x$ is the independent variable.
• $b$ is the y-intercept.

Match that up to the general form:

$y = 4 x - 2$

$\implies m = 4$
$\implies b = - 2$

This means the slope describes an increase in $y$ of $4$ for every increase in $x$ of $1$:

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{4}{1}$

This also means that the graph crosses the $y$ axis at $y = - 2$, the y-intercept where $x = 0$. This means that:

• $\left(0 , - 2\right)$ is a point on the graph.
• Applying the slope onto $\left(0 , - 2\right)$, we get that $\left(0 + 1 , - 2 + 4\right) = \left(1 , 2\right)$ is another point on the graph.

Two points make a line, so you have your graph:

graph{4x - 2 [-10, 10, -5, 5]}

And you should spot where $\left(1 , 2\right)$ is on the graph to verify that it is there.