How do you find the equation of a line when given a containing point and slope?

Answer 1

If you know the slope (m) and a point which we'll call x1, y1 then the equation of the line can be found by using the formula y - y1 = m(x - x1)

Input the know values and then bring all the unknowns (x and y) to the left hand side and the knowns (the numbers) to the right hand side.

For example:

* Find the equation of the line that passes through the point (-2 , 5) and has a slope of -4. * Substitute y1 , x1 and m in the point slope form of a line * y - y1 = m(x - x1) * y - 5 = - 4(x - (-2)) <--- If 'm' is a fraction - multiply both sides by the denominator * y = - 4x - 3 * 4x + y = -3

* I am just not getting it. I know you use the point slope equation, but I just dont get the ending. * The problem is: * m=8/9, (3,-4) * I get the point slope equation... which makes it * y+4=8/9x-3 * Now what do I do... Can someone break it down step by step (I am just not understanding) multiply both sides by 9 to remove the fraction

9y + 36 = 8x - 27

Bring the y value to the other side - i.e. subtract 9y from both sides

36 = 8x - 9y - 27

get all the numerical values to the same side - i.e. add 27 to both sides

36 + 27 = 8x -9y

63 = 8x - 9y

swap everything around to produce the standard format for an equation....

8x - 9y = 63