Slope of a line 8.F.2 COMPARE properties of two functions each REPRESENTED in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Slope describes the slant or direction of a line.

Given two points (x1, y1) and (x2, y2), the formula to find the slope of the straight line going through these two points is:

Slope The subscripts in each ordered pair indicate that one is a "first" point and the other is a "second" point . 

Slope Slope also called “rate of change” and sometimes referred to as “rise over run“. The slope fraction consists of the "rise" (change in y, going up or down) divided by the "run" (change in x, going to the left or right).

The two points shown are: (0, -4) and (-3, -6) The two points shown are: (0, -4) and (-3, -6). Now we have two points we can put them in the slope formula:

Example #2

Find the slope: (-3, 6) and (5, 2)

Slope There are four possibilities for the slope of a line: y y x x Positive Slope x y m > 0 Line rises from left to right. Negative Slope x y m < 0 Line falls from left to right.

Horizontal Lines The points (-3, 4) and (5, 4), the slope is: For every horizontal line, a slope of zero means the line is horizontal, and a horizontal line means you'll get a slope of zero. The equation of all horizontal lines is of the form y = “a number” (ex. y = 4)

Vertical Lines Now consider the vertical line of the equation x = 4: A vertical line will have no slope, and “the slope is undefined" means that the line is vertical.  The equation of all vertical lines is of the form x = “a number” (ex. x = 4). 

The other two possibilities for the slope of a line: Zero Slope x y m = 0 Line is horizontal. m is undefined Undefined Slope x y Line is vertical.

Find the slope of a line that contains points: (5, 4) and (5, 2). This slope is undefined.

Find the Slope Red (3, 9) Blue (11, 2) Green (5, -2)

Are we going too fast? Let’s review!

If I am given a line on the coordinate plane, how do I find the slope? Q & A If I am given a line on the coordinate plane, how do I find the slope? Pick any two points on the line and use the slope formula OR Find the “rise” (change along the y-axis) and the run (change along the x-axis.

No, the math will be different, but the answer will be the same. Q & A If I pick two different points than someone else won’t I get a different answer? No, the math will be different, but the answer will be the same.

First pick any two points on the line. (5,6) (-4,-2) First pick any two points on the line. Then find the coordinates of the points and use them in the slope formula.

Key Skills y Graph the points (0, 400), (15, 250) 1000 Graph the points (0, 400), (15, 250) 500 Does the direction of the line show a positive or negative trend? x -20 -10 10 20 -500 Negative. -1000 Find the slope.

Key Skills TRY THIS Edgar deposited $100 in the bank. After 6 weeks he had deposited a total of $220. Graph the amount of money he has in his account, then find the slope. What are the 2 sets of (x, y) coordinates? (0, 100) (6, 220)

Does the direction of the line show a positive or negative trend? x TRY THIS Key Skills y 250 Graph the points (0, 100), (6, 220) 125 Does the direction of the line show a positive or negative trend? x -10 -5 5 10 -125 Positive. -250 Find the slope.

Key Skill m = y2 – y1 (0, 100) ( 6, 220) x1 y1 x2 y2 x2 – x1 . m = y2 – y1 (0, 100) ( 6, 220) x1 y1 x2 y2 x2 – x1 Label the coordinates m = 220 – 100 120 = = 20 6 - 0 6 Substitute into the formula The slope = 20