Question

Find the equation of the line given two points. (2,1), (5,2). y=?

example answer: (4,0), (5,2). y=2x-8

please help. ive been on this problem for almost an hour now

Answer 1

Answer:
`y = (1)/(3)x+(1)/(3)`
Note: the slope is 1/3 and the y intercept is 1/3

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Step-by-step explanation:

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
`y = (1)/(3)x+(1)/(3)`