How do you write the equation in point slope form given (1, 3) and (4, 4)?

1 Answer
thelittlestleafeon
Mar 5, 2018

#y=1/3x+8/3#

Explanation:

Recall that the equation for a line in point-slope form is #y=mx+b#, where m is the slope and b is the y-intercept.
First we have to find the slope using #m=(y-y_1)/(x-x_1)# (second point minus first point).
Plugging in (4,4) for (x,y) and (1,3) for #(x_1,y_1)#, we get #m=((4)-(3))/((4)-(1))=1/3#.
We now have the equation #y=1/3x+b#.
Next, let's plug in a point and solve for b. I will use the point (1,3).
#(3)=1/3(1)+b#
#b=3-1/3=9/3-1/3=8/3#.

With both our slope and y-intercept, we can now write the equation of the line as:
#y=1/3x+8/3#

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