First, Some Important slides from last time! Take Some Notes! Slope and Stuff First, Some Important slides from last time! Take Some Notes!

= Change in y = = Change in x = Slope Intercept Form for a Line with a Slope of m and a y-intercept of b is… Y-int. Slope Slope describes a lines its steepness, incline, decline or grade. = Change in y = = Change in x =

What the Slope? = Change in y = = Change in x = Slope describes a lines its steepness, incline, decline or grade. = Change in y = = Change in x =

How do we calculate Slope With 2 Points? If we have a point (x1, y1) and another point (x2, y2), how can we calculate slope? Change in y (rise) over the Change in x (run). It looks likes this. (x2, y2) (x1, y1)

Example #1 If we have a point (x1, y1) and another point (x2, y2), how can we calculate slope? (x2, y2) (3, 3) (x1, y1) (0, 0) = m

Example #2 If we have a point (x1, y1) and another point (x2, y2), how can we calculate slope? (x2, y2) (3, 1) = = m (1, -2) (x1, y1)

Example #3 If we have a point (x1, y1) and another point (x2, y2), how can we calculate slope? (x1, y1) (-2, 1) = = (x2, y2) (2, -2) = m

Using Example #1 m = What is the y intercept? How do we find it? Our equation is y = x + b (remember m = 1) We have 2 Points! (3,3) and (0,0). Lets just plug one of them into our equation. Which is easiest? (x2, y2) (3, 3) (x1, y1) (0, 0) y = x + b 0 = 0 + b (0,0) 0 = b So… y = x + 0 or… y = x!!

Find the y-int of example #2 Our two points = = m (3, 1) (1, -2) (x2, y2) Our equation (3, 1) What point to plug in? (3, 1) (1, -2) (1, -2) (x1, y1)

What is our equation for (3, 1) and (1,-2) then? = m Yay! Yay! Yay! Yay! Yay! Yay! Yay! Yay! Yay!

Lets talk about the x-intercept! So the y-intercept is where the line goes through the y axis, so the x-intercept is when Our line goes through the x axis. They go through points: Our y-int. (0,1) Our x-int. (-1,0) Interesting… so y is zero for the x-int! Lets find the x-intercept for an equation!

Example #4 Find the x-intercept of: (x,0) y = x + 5 0 = x + 5 -x -x Lets find the x-intercept for a harder equation!

Example #5 Find the x-intercept of: (x,0) y = -0.5x - 3 0 = -0.5x -3 /0.5 /0.5 x = -6 Is our x-intercept! (-6,0)

Vertical/Horizontal Line Discussion What is the x-intercept of this vertical line? It’s -3!! So when y = 0, x = -3! What about when y = 2? It’s also -3! It’s -3 everywhere! So, x is not dependant on y, Therefore our equation of the line is x = -3

Vertical/Horizontal Line Discussion What is the y-intercept of our vertical line? Our equation of the line is x = -3 So, there will be no y-int Sorry y-int…

Vertical/Horizontal Line Discussion What is the slope of our vertical line x = -3? Let’s think about rise over run first. Can’t divide be zero… Lets try 2 points, (-3,2) and (-3,0) Can’t divide be zero

Vertical/Horizontal Line Discussion What is the slope of our vertical line x = -3? our slope is Undefined. All vertical lines have an undefined slope. Sorry slope

Vertical/Horizontal Line Discussion What is the x-int and y-int of a horizontal line? y-int is 3. in fact, its 3 everywhere! x-int does not exist. So y = 3

Vertical/Horizontal Line Discussion What is the slope of a horizontal line y = 3? Let’s think about rise over run first. Cool… Lets try 2 points, (1,3) and (2,3)

Vertical/Horizontal Line Discussion What is the slope of our horizontal line y = 3? our slope is 0. All horizontal lines have a zero slope.