# How do you graph y=5x-5/2 using slope and intercept?

Feb 16, 2018

See below.

#### Explanation:

Use the general equation of a line:

$\textcolor{red}{y = m x + b}$

Here, $m$ is the slope of the line. It states that, for every change in the $x$ coordinate by $1$ unit, the $y$ coordinate changes by $m$ units. Its formula is:

$\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$.

Here, $m = 5$.

$b$ is the $y$-intercept, the value of $y$ when the line intercepts the $y$ axis. Here, the $b = - \frac{5}{2}$

Through the observations above, we find that:

• The line gets to $x = 0$ at $y = - \frac{5}{2}$
• After that, for every $1$ unit increase in the $x$ value, the $y$ value increases by $5$ units.

So at $x = 0$, $y = - \frac{5}{2}$

At $x = 1$, $y = \frac{5}{2}$

At $x = 2$, $y = \frac{15}{2}$

At $x = 3$, $y = \frac{25}{2}$

And so on and so forth. We can use Socratic's graphing utility to make sure of so:

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

We can see that our observations are true.