First we need the slope of the line through the two points. Use the slope formula
m = (y2 - y1)/(x2 - x1) m = (2-1)/(5-2) m = 1/3
The slope is m = 1/3
Use this slope, along with one of the points. I'll use the point (x,y) = (2,1). Plug these three values into the equation y = mx+b and then solve for b
y = mx+b 1 = (1/3)(2)+b 1 = 2/3+b 1-2/3 = 2/3+b-2/3 1 - 2/3 = b b = 1 - 2/3 b = 3/3 - 2/3 b = 1/3
So the slope and y intercept are m = 1/3 b = 1/3
Therefore the equation is [tex]y = \frac{1}{3}x+\frac{1}{3}[/tex]
