which of the following is a point slope equation of the line below (10,5)(2,2)
Accepted Solution
A:
Point slope form follows the equation y-y₁=m(x-x₁), so we want it to look like that. Starting off with m, or the slope, we can find this using your two points with the formula [tex] \frac{ y_{1} -y_{2} }{ x_{1} - x_{2} } [/tex]. Note that y₁ and x₁ are from the same point, but it does not matter which point you designate to be point 1 and point 2. Thus, we can plug our numbers in - the x value comes first in the equation, and the y value comes second, so we have [tex] \frac{5-2}{10-2} = \frac{3}{5} [/tex] as our slope. Keeping in mind that it does not matter which point is point 1 and which point is point 2, we go back to y-y₁=m(x-x₁) and plug a point in (I'll be using (10,5)). Note that x₁, m, and y₁ need to be plugged in, but x and y stay that way so that you can plug x or y values into the formula to find where exactly it is on the line. Thus, we have our point slope equation to be [tex]y- 5= \frac{3}{5} (x-10)[/tex]