Mathew D. answered • 05/01/13

Science, Math & More

Linear equations are the first step to understanding how graphing works. The default equation which will shortly become permanent in your knowledge of math is: y = mx + b

This equation is the slope-intercept form for straight lines where 'm' represents the slope of the line, and 'b' represents the y-axis intercept (when x = 0, y = b).

Using your example, let's first change the equation to be in the slope-intercept form.

x + 2y = 6 [beginning equation]

2y = -x + 6 [subtracting 'x' from each side]

y = -x/2 + 6/2 [dividing each side by 2]

y = -1/2x + 3 [simplify]

Now the equation is in slope-intercept form. From the equation now, we can tell that the **slope** (m) is -1/2 and the y-axis **intercept** (b) is 3.

An easy first point is the intercept, so (0,3) could be your first point. From there you can either draw a straight line at a slope of negative 1/2 (which is to say for every 2 points you move right on the x-axis, you'll drop down 1 on the y-axis). Or you can input any value for x and find it's corresponding point on y by solving the equation. Making a table can help with that:

__x__|__y__

0 3

2 2

6 0

*a few examples, but any 'x' value would be fine.

Sharan D.

03/15/16