Introduction To Slope

OBJECTIVE: The students will be able to find the slope of a line given 2 points and a graph.

What is the meaning of this sign? Icy Road Ahead Steep Road Ahead Curvy Road Ahead Trucks Entering Highway Ahead

Slope is a measure of Steepness.

Types of Slope Zero Negative Positive Undefined or No Slope

Slope is sometimes referred to as the “rate of change” between 2 points. The rate of change must be constant

Determine the slope of the line. When given the graph, it is easier to apply “rise over run”.

Example 1: Determine the slope of the line Start with the lower point and count how much you rise and run to get to the other point! rise 3 = = 6 run 6 3 Notice the slope is positive AND the line increases!

used to represent slope. The letter “m” is used to represent slope. Why?

If given 2 points on a line, you may find the slope using the formula m = y2 – y1 x2 – x1

The formula may sometimes be written as m =∆y . ∆x What is ∆ ? Change

Example 3: Find the slope of the line through the points (3, 7) and (5, 19). y1 x2 y2 m = 19 – 7 5 – 3 m = 12 2 m = 6

Example 4: Find the slope of the line through (-3, 2) and (-6, -2) -6 – (-3) m = -4 -3 m = 4 3

This means there is ZERO SLOPE= a horizontal line. What if the numerator is 0? 0 # = 0 This means there is ZERO SLOPE= a horizontal line.

This means there is NO SLOPE= a vertical line. What if the denominator is 0? # 0 = undefined This means there is NO SLOPE= a vertical line.

If given an equation of a line, there are 2 ways to find the slope and y-intercept.

One method is to write the equation in slope-intercept form, which is y = mx + b. slope y-intercept

y = 3x + ½ Find the slope and y-intercept of the following equations.

First, solve the equation for y. 3x + 5y = 10 First, solve the equation for y. 3x + 5y = 10 5y = -3x + 10 y = -3/5 x + 2 m= -3/5 b = 2

The End