HA1-385: Finding the Slope of a Line

What is SLOPE? Slope, in math, describes the STEEPNESS of a line. How is slope used in LIFE???? Skiers LOVE good slope. The steeper the slope, the faster you go!!

What is SLOPE? Slope is STEEPNESS of a line. Amusement park engineers use slope to design rides.

What is SLOPE? Slope is STEEPNESS of a line. Home builders & architects use it to design homes. A roof has slope.

What is SLOPE? Slope is STEEPNESS of a line. Road builders use slope to design roads that rain will run off.

How do we use slope in Algebra class? We look at lines to learn about steepness ( slope) so we can apply our knowledge later. When you graph a line, you need x’s and y’s. A lot of equations we use have two variables, an x and a y. These equations represent lines we can graph.

How do we use slope in Algebra class? Equations can look like y=3x+5 , which could represent the situation “you pay $5 to get into the arcade, and then $3 for every game you play” , - It can be graphed to represent ALL of the different combinations of # of games played .

How do we use slope in Algebra class? Equations that look like y=3x+5 can be graphed. We will learn how to graph these equations in a future lesson.

How do we use slope in Algebra class? Equations can look like -3x + y=5 . We will how to transform these equations into a “y=mx + b” equation called slope intercept form. This is the EASIEST equation to graph from and will be your FRIEND. Let’s Learn!

m = m = (y2−y1) (x2−x1) rise run What we will learn in THIS lesson 1. To find the slope from TWO points like ( 2,3) and (1,4) using 2. To find slope from a graph using (y2−y1) m = (x2−x1) M is the variable letter used to represent SLOPE rise m = run

The slope (m) of a line describes its steepness. It is determined by its: a) vertical change (or rise) b) horizontal change (or run)

A line that moves upward from left to right has a positive slope. I’m positive this uphill is hard work A line that moves downward from left to right has a negative slope. WEE….this downhill is easy, don’t be so negative.

Two lines that have the same slope are parallel. Horizontal lines have a slope of 0. Vertical lines have an undefined slope.

The slope (m) of a line is measured by the vertical change in y or (rise) over the horizontal change in x or (run). m = change in y change in x or rise m = rise run run

You can find the slope (m) of a line by using the rise and the run of the line. 1 4 8 ft. The slope of the ramp is 1/4.

You can find the slope (m) of a line by using the coordinates of any 2 points on the line to find the change in y and the change in x. y x (y2−y1) or rise (x2, y2) m = (x2−x1) or run (x1, y1)

m = m = y2 − y1 x2 − x1 (2) − (−1) + m = 3 4 ( 2) − (−2) + Find the slope (m) of a line passing through the following points by finding the change in y and the change in x. (x1,y1) (x2,y2) A (-2,-1), B (2,2) m = y2 − y1 x2 − x1 (2) − (−1) + ( 1) m = 3 4 m = ( 2) − (−2) + ( 2) The slope of the line is 3/4 .

m = m = m = y2 − y1 x2 − x1 (−2,-2) & (3,0) 0 − (−2) 2 2 5 3 − (−2) 2 Find the slope (m) of a line passing through the following points by finding the change in y and the change in x. (x1, y1) (x2,y2) m = y2 − y1 x2 − x1 (−2,-2) & (3,0) 0 − (−2) + 2 m = 2 5 m = 3 − (−2) + 2 The slope of the line is 2/5 .

m = m = m = y2 − y1 x2 − x1 (-3,3) & (3,−2) −2 − 3 −5 6 3 − (−3) 3 Find the slope (m) of a line passing through the following points by finding the change in y and the change in x. (x1, y1) (x2, y2) m = y2 − y1 x2 − x1 (-3,3) & (3,−2) −2 − 3 3 m = m = −5 6 3 − (−3) 3 + The slope of the line is − 5/6 .

Zero Slope m = = = x y y2 − y1 3 − 3 x2 − x1 5 − 2 3 ZERO Slope, like the worst ski slope ever! OR graphed OR from two given points ( 2, 3) and ( 5, 3) = Where’s the hill?? Zero slope graphed. y x Zero slope Zero slope m = y2 − y1 x2 − x1 3 − 3 5 − 2 3 = =

No Slope or Undefined Slope I am heading into undefined territory!! Yahoo!! No or Undefined Slope is like a CLIFF! Same as undefined slope No slope graphed. No SLOPE from two given points, (-4, 3) and (-4, -2) Undefined slope. So STEEP, it has NO SLOPE!! m = y2 − y1 x2 − x1 -2 − 3 -4 − -4 -5 = = = No Slope

m = m = rise run x The slope of the line is 3/4 . y Find the slope (m) of this line by finding the rise and the run of the line: m = rise run y x (2, 2) 3 m = 4 (−2, −1) The slope of the line is 3/4 .

m = m = rise run x The slope of the line is − 5/6 . y Find the slope (m) of this line by finding the rise and the run of the line: m = rise run (−3, 3) y x −5 m = 6 The slope of the line is − 5/6 . (3, −2)

Take a Look………….. Think about this! The next two slides aren’t in THIS lesson, but you will have to do them very soon…… Take a Look…………..

Graph the line that contains the point (−2,−2) and has a slope of m = 2 rise 3 run A second point on the line is (1, 0). Use the two points to graph the line. (1, 0) (−2,−2)

Graph the line that contains the point (−3,2) and has a slope of . m = −3 rise 5 run (−3,2) A second point on the line is (2,− 1). Use the two points to graph the line. (2, −1)