Wed, 12/7 SWBAT…compute slope Agenda WU (10 min) Notes on slope (35 min) Warm-Up: 1. HW#3: Slopes of lines (front & back) 1

How do engineers build bridges?

How do engineers build roads?

How do builders build roofs?

How can we write 7% as a fraction?

7% as a fraction?? Remember than any percent is a part of 100.

The grade or incline of a road is the same as slope Here is the picture: 7 feet 100 feet

Slope of a line (m) To find the slope, use the formula (elevacion) 4 (elevacion) (desplazamiento) 4

Slope of a line (m) To find the slope, use the formula 4 4

Slope of a line (m) Find the slope of the following lines: A) B) 2 2 1 3

Why do we use m for slope? Possibly because m comes from the French word “monter”, which means to climb The earliest textbooks used m, and everyone else just copied it

Slope of a line (m) Is the slope positive or negative? Answer: Positive, read from left to right

Try for yourself Using the graph paper squares, draw lines with the following slopes. Start anywhere on your coordinate plane. A) B) Label your lines with their slopes Glue the graphs in your note book

Slope of a line (m) The last 2 lines had a positive slope, let’s look at slopes with negative slopes

Slope of a line (m) We still use rise over run, except the “stairs” are underneath the line. -2 3

Try for yourself Using the graph paper squares, draw lines with the following slopes. Start anywhere on your coordinate plane. C) D) Glue the graphs in your note book

Your turn Slope = 2/4 = 1/2

“Official” Definition of Slope Slope is the change in the vertical distance (rise) over the change in the horizontal distance (run) Pendiente: Razon del cambio en la coordenada y (elevacion) al cambio correspondiente en la coordenada x (desplazamiento) a medida que uno se mueve de un punto a otra en una recta.

Question Find the slope of the line that passes through (1, 0) and (-1, -1). (x1, y1) (x2, y2) (To see the slope visually… Plot these points. Connect the line (don’t forget arrows)). m = (y2 – y1)/(x2 – x1) = (-1 – 0)/(-1 – 1)) = -1/-2 m = 1/2

What the graph looks like 1 2 m =

Find the rate of change: x y 2 1 4 6 -1 m = (y2 – y1)/(x2 – x1) = (2 – 1) / (0 – 2) = 1/-2 = -1/2

  Directions: Find the value of r so the line that passes through each pair of points has the given slope. (12, 10), (-2, r) m = -4 r = 66

Horizontal lines have a slope of ___ Vertical lines have a slope of ___ m = 0 Vertical Horizontal m = undefined

Practice Problem A horizontal lines passes through (2, 5). What other point does the line contain? (2,3) (0,5) (5,10) (0,2)