I cannot remember how to find the slope of a line when you are given two points.

Question

Here is the problem.

The slope of a line through (2,1) and (5,n) is 3. n=___

I ended up with -2. But I don't think that is the right answer. I put the points in slope-intercept form and solved for y, which would end up being n, right?
y(or n)=5x+3
y(1)=2x+3 [x equals -1 right?]

I'm so confused. . . .

Answer 1

How would you find slope if you knew all of the two points

just set

(n-1)/(5-2)=3
n-1 = 9
n = 10

test is by finding the slope, it works

Answer 2

the method you tried will work, but you made an error.

here is how it would have looked:

let y = mx + b, but we have a point (2,1) and m=3
1 = 3(2) + b
b = -5

so the equation is y = 3x - 5

now sub in (5,n)
n = 3(5) - 5
n = 10

much longer and more complicated, you must agree.