What is slope and how is it determined from a graph?

Think of a straight line that heads up as x increases. By how much does y increase as x increases by 1? The answer is the "slope" of the line, also referred to as the "rate of change of y with respect to x," and calculated by using the formula

rise

m = slope =

run

If you're starting with such a straight line graph on a grid (consisting of horizontal and vertical lines, all equally spaced), try to identify a point on the line that goes exactly through the intersection of one horiz. and one vertical line from this grid. If, for example, the vertical line represents x=2 and the horiz. line represents y =3, then the point on the line would be (2,3). Try to identify one other point on the line and to identify its coordinates similarly.

By how much does x change? That's the "run." Write that number in the denominator of the fraction

m = rise / run. By how much does y change? That's the "rise." Write that number in the numerator of the fraction.

Then you have the slope of the straight line, m = rise / run.

This procedure is only slightly harder if the line descends instead of ascends as x increases.

y > 1/3x

y < = -x + 4

hope this : )