How do you find the slope of # 3y=x+3#?

1 Answer
Acquaintance
Jul 13, 2016

Slope: #1/3#

Explanation:

Slope-intercept form: #y=mx+b#; where #m# is the slope.

If we put the given equation into slope-intercept form, we can identify the slope.

First get #y# all by itself.

#3y = x+3#

#y = x/3 + 1#

This equation is now in slope intercept form. We must find the slope. We saw at the top that the slope, #m#, comes right before the variable. Here is our variable term:

#x/3#

It is in the form of a fraction. What do we do to clearly identify the slope? Rewrite the variable term, since #x/3# is the same as #1/3 times x#.

#x/3 = 1/3 times x = 1/3 x#

Now let's rewrite the whole equation.

#y = 1/3 x + 1#

#color(grey)(y = mx+b)#

Look for the number before #x#, or the number combined with it. In this case, the slope appears to be #1/3#.

If we were to graph the equation and look at the slope that way, it would be the same.

graph{1/3x+1 [-10, 10, -5, 5]}

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