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]}