Question

STRUCTURE Find the slope of the line that passes through the pair of points. (0,1) (2,5)

Answer 1

Answer: There are 2 equation, but both of them are the same line. They are

`y-1=2x` and

`y-5=2(x-2)`.

Step-by-step explanation: We can get out answer by using point-slope form, which is

`y-y_(1) =m(x-x_(1) )`, with y1 and x1 being one of the points (in this case, either 0 or 2 work for x1 and 1 or 5 work for y1). We can find the slope by using the slope formula, which is

`m=(y_(1) -y_(2) )/(x_(1)- x_(2) )`, so y1 would be 5, y2 would be 1, x1 would be 2, and x2 would be 0. (You can swap y1 and y2 as long as you also swap x1 and x2). Using this, we would get

`m=(5-1)/(2-0) =(4)/(2) =2` so our slope of the line is 2. Now that we have our slope, and our points were given, we can plug them into the point-slope form and get

`y-1=2x` if you plug in 2 as y1 and 0 as x1, and you get

`y-5=2(x-2)` if you plug in 5 as y1 and 2 as x2.

NOTE: These two equations are the same.