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# how do you graph equations?

Two lines are parallel if they have the same slope. Transform the equations into the slope-intercept form

y=mx+b

, then compare the values of m.

- If the lines are parallel, the values of m will be the same

- if the lines are perpendicular, one value of m will be the negative reciprocal of the other. That is, if m = 2, a perpendicular line would have slope m=-1/2

- if the lines fit neither of the above conditions, then the lines intersect but are neither parallel or perpendicular.

Regarding graphing, once the equation is in slope intercept form, you can plot the point (0, b) as your y intercept, then either

(a) Pick x values and calculate the corresponding y, or

(b) use your slope to determine your next point. Since slope is defined as rise over run (change in y divided by change in x), you can use it to determine the next point.

Example: If my equation was y=2x+5, then my y-intercept is (0,5), and the slope of 2 indicates that I add 2 to my y value for every 1 I move to the right in my x value. So my next point in this example would be (1,7) [0+1, 5+2], and my next point could be (2,9) [that is, 1+1, 7+2], and so on.