This week in math 10 we learned different forms of equations based on slope. One equation was the slope y-intercept ( y = mx + b, where m is the slope of the line and b is the y-intercept), another equation was general form (Ax + By + C = 0 where this equation has no relation to y intercepts or slopes. Not the most useful equation), the last equation is the slope-point form y-y₁=m(x-x₁) where m is the slope and y1 and x1 are one coordinate that the line goes through. The easiest and most useful equation. These equations are all easy to change into each other.

Slope-Point Form to Slope Y-Intercept Form to General Form

If we are given coordinates (-4,2) and the slope -1/3

First we figure out which equation to use and I chose slope=point form because we are given the variables needed to complete the formula.

m(x-x1)=y-y1

-1/3(x+4)=y+2

Now we distribute

-1/3x – 4/3 = y+2

Thenwe just solve the most we can

-1/3x – 10/3 =y

Now we already have it in slope y-intercept

Then to general form we need to multiply everything by the denominator which is 3 for both of them

-x -2 = 3y

Now we need y to equal a 0 so we could subtract 3y from both sides but we want x to be positive so I am going to take -x and -2 and switch them to the other side of the equal sign

x+3y+2=0

That’s in general form