How do you graph y = 3x + 5?

Apr 9, 2016

graph{3x+5 [-10, 10, -5, 5]}

$x$ intercept: $x = - \frac{5}{3}$
$y$ intercept: $y = 5$

Explanation:

For a linear graph, the quickest way to sketch the function is to determine the $x$ and $y$ intercepts and draw a line between the two: this line is our graph.

Let's calculate the $y$ intercept first:

With any function, $y$ intercepts where $x = 0$.
Therefore, substituting $x = 0$ into the equation, we get:

$y = 3 \cdot 0 + 5$
$y = 5$
Therefore, the $y$ intercept cuts through the point (0,5)

Let's calculate the $x$ intercept next:

Recall that with any function: $y$ intercepts where $x = 0$.

The opposite is also true: with any function $x$ intercepts where $y = 0$.

If we substitute $y = 0$, we get:

$0 = 3 x + 5$
Let's now rearrange and solve for $x$ to calculate the $x$ intercept.

$- 5 = 3 x$
$- \frac{5}{3} = x$
Therefore, the $x$ intercept cuts through the point $\left(- \frac{5}{3} , 0\right)$.

Now we have both the $x$ and $y$ intercepts, all we have to do is essentially plot both intercepts on a set of axis and draw a line between them

The graph of the function $y = 3 x + 5$:

graph{3x+5 [-10, 10, -5, 5]}