How do you graph y = 3x + 5?

1 Answer
Apr 9, 2016

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

x intercept: x=-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*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=3x+5
Let's now rearrange and solve for x to calculate the x intercept.

-5=3x
-5/3=x
Therefore, the x intercept cuts through the point (-5/3,0).

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=3x+5:

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