Scalar+Equations

Also known as the standard form, scalar equations are another way of writing linear relations. They are written in the form: Ax + By = C


 * Level I: Graphing using intercepts (review intercepts)**

Intercepts are the points where graphs intersect the x- and y- axes. Graph the lines with the following intercepts:

a) x = 3, y= 6

b) x = -2, y = 3

c) x = 5, y = -4

d) x = -4, y = -5


 * Level II: Determining intercepts and graphing**

In order to determine the intercepts, set the other co-ordinate to zero.

e.g. to find the x-intercept, set y = 0

e.g. 2x-3y = 6 2x - 3(0) = 6 2x = 6 x = 3

e.g. to find the y-intercept, set x = 0

2x - 3y = 6 2(0) - 3y = 6 -3y = 6 y = -2


 * Level III: Converting Scalar form to slope-intercept form**

Reminder: The slope-intercept form looks like: y=mx+b where m is the slope and b is the y-intercept

2x-3y=6 -3y = 6 - 2x [move the x-term to the other side] y = -2 + 2/3 x [divide by -3 in order to isolate y] y = 2/3 x - 2 [re-arrange so that the x-term is in front]


 * Level IV: Converting slope-intercept to Scalar form**

y = 3/4x + 5 4y = 3x + 20 [multiply each term by the denominator] -3x + 4y = 20 [move the x-term to the other side] 3x - 4y = -20 [multiply all terms by -1 if necessary in order to make sure that the x-term is positive]