The ratio of the vertical change to the horizontal change SLOPE The ratio of the vertical change to the horizontal change

Slope is the measure of the steepness of a line! IN LAYMAN’S TERMS: Slope is the measure of the steepness of a line!

HOW IT’S FIGURED: there are two ways Also know as: Rise Run VERTICAL CHANGE ___________________ STEEPNESS = HORIZONTAL CHANGE **OR** Change in Y-axis ___________________ SLOPE (m) = Change in X-axis

Find the slope of the hill

Find the slope of the hill

And the answer is…. 3 2.5

Find the Slope of the Slide

Find the Slope of the slide

And the answer is… 4 or 2 2 1

Find the slope of the rollercoaster

Find the slope of the rollercoaster

And the answer is…. 7 - 2.5

Find the slope of the mountain

Find the slope of the mountain

And the answer is…. 5 - 4

Solve by graphing: • A line goes through points (-3,5) and (2,1)

• Start at the left dot and count down till you’re To solve by graphing: • Start at the left dot and count down till you’re even with the right dot.

• Start at the left dot and count down till you’re To solve by graphing: • Start at the left dot and count down till you’re even with the right dot.

• Now count over till you reach To solve by graphing: • Now count over till you reach the right dot.

And the answer is…. 4 down, 4 to the right -4 5

To solve by formula, simply replace the x and y values with the x and y values of the points. (-3,5) and (2,1) y1 – y2 x1-x2 Hint! (-3[x1], 5[y1]) and (2 [x2], 1 [y2]

And the answer is… 5 – 1 4 -3 – 2 -5 There the same answer!

WORK TIME! In your groups Find the slope of a line that contains points A(-2, 5) B(4, -5)

HERE’S HOW YOU SOLVE IT: Change in Y-axis ___________________ SLOPE (m) = Change in X-axis 5 – (-5) ___________________ m of line AB = -2 - 4 10 ___________________ = -6 5 ___________ - = 3

NOW TRY THESE ON YOUR OWN Find the slope of a line that contains each pair of points: R(9, -2) S(3, -5) M(7, -4) N(9, 4)

True or False?? ALL HORIZONTAL LINES HAVE THE SAME SLOPE

TRUE! All horizontal have a slope of 0

What is the slope of the wall?

The slope of a vertical line has NO SLOPE!

CAN TWO LINES HAVE THE SAME SLOPE?

Parallel lines have the same slope YES! Parallel lines have the same slope

It’s a Miracle! Slope Intercept Form y= mx + b X- x value Y- y value M- the slope B- y intercept ( we will learn about this tomorrow)

Slope Intercept Form In the equation: Y= 2x + 5 2 is the slope What is the slope of the line of: Y= 2/3x + 8?

Classifying Slope Positive slope – line slants up from left to right. • Negative slope – line slants down from left to right. • Zero slope – line is horizontal. • Undefined slope – line is vertical.

Try with your group: X Y What is the slope of the line represented by the table of values below? -20 1 -10 2 3 10

Try with your group: What is the slope of the line represented by the equation below? y =    1/2  x + 3  

Try with your group: B A D C Which of the following shows the graph of a line with positive slope? B A D C

                                                                                                             Which statement best describes the slope of the line graphed above? Try with your group:   A. The slope is −6. B. C. The slope is       D. The slope is 4. The slope is -     

Which of the following lines appears to have the greatest slope?