This week in Math 10 we learned 3 different about line equations and how to write them. Some of these came off as hard to do when we started but the more we did all of them the more I understood lines and slope in general.
Slope Y-Intercept Form:
This form can be written as y=mx+b where the mx is the slope and b is the y intercept.
Example:
If we know the slope of a line is 2 and the Y-intercept is (0, 6) you can write the equation as y=2x+6.
General Form:
This form can be written as Ax+By+C=0, this is found by taking an equation in Slope Y-intercept form and getting rid of any fractions while also moving the Y to the other side. This form does not tell us anything about the graph so the only way you can use it is to convert it to Slope Y-Intercept Form.
Example:
If I have something in Slope Y-Intercept form such as y=3/4x+5, to write it in general form I would need to get a rid of the fraction by multiplying everything by four to get 4y=3x+20. Now I need to get the y to the other side, so in the end I would get 0=3x-4y+20.
Slope-Point Form:
Slope point form is the easiest way to write an equation of a line with. All you need is one nice point on the line and the slope of it. You can write it as m(x-x1)=y-y1
Example:
If I have a slope of 3 and one of lines coordinates such as (6, 1) I can write it as:
3(x-6)=y-1