What is the equation of the line passing through #(4,5), (5,7)#?

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Answer 1 · 2018-03-06T00:04:35

Given two points, we can calculate the slope using the formula #m = \frac (y_2-y_1)(x_2-x_1)#.

So, #m = \frac (7-5)(5-4)#, which simplifies to #\frac2 1#, or just #2#.

Knowing this, we can substitute numbers into slope-intercept form (#y=mx+b#). Either point will work for this, but I used the first one just because:

#5=2(4)+b#

Now we simplify:
#5=8+b#

Subtract 8 from both sides to isolate b:
#-3=b#

Now that we have the y-intercept, we can write the equation:
#y=2x-3#.