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

1 Answer
Mar 6, 2018

Slope-intercept form: y=2x-3

Explanation:

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.