12-6 Class notes - Standard form of a linear equation

(  ,  ) indicates an ordered pair, contains an x and a y, suggests the shape of a point

(  ,  ), (  ,  ) indicates two ordered pairs, has the four values needed to find a slope, suggests a line

m indicates a rate, a slope, a measure of slant, a rise over a run; m stands next to the x

b indicates the height above the origin, it's the y-intercept, it gives the point (0, b)


The slope-intercept form  y = mx + b has the variable y by itself on one side of the = sign.

The standard form Ax + By = C has the constant C (a number) by itself on one side of the = sign.



A is the coefficient of x (a number that multiplies x)
B is the coefficeint of y (a number that multiplies y)

To change from slope-intercept form to standard form, isolate b, the y-intercept.  Move the mx term to the other side of the equal sign.



To change from standard form to slope-intercept form, move the Ax term away from the By term.  Divide both sides by B.  m, the slope, will be -A/B and b, the y-intercept, will be C/B.