1.2: Slope -slope formula M(G&M)–10–9 Solves problems on and off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope. GSE

Understanding Slope If a line rises as you move from left to right, then the slope is positive. Riding a bike uphill

Understanding Slope If a line drops as you move from left to right, then the slope is negative. Skiing Downhill

Understanding Slope A horizontal line has zero slope: m = 0 Running on a flat surface like a track Or any athletic field Running on a flat surface like a track Or any athletic field Running on a flat surface like a track Or any athletic field

Understanding Slope A vertical line has no slope: m is undefined. Running into a wall, you cant get past it Running into a wall, you cant get past it

Slope Formula The slope of a line through the points (x 1, y 1 ) and (x 2, y 2 ) is as follows: y2 – y1y2 – y1x2 – x1x2 – x1y2 – y1y2 – y1x2 – x1x2 – x1 m =

Ex. Find the slope of the line that passes through (–2, –3) and (4, 6). Let (x 1, y 1 ) be (–2, –3) and (x 2, y 2 ) be (4, 6). 6 – (–3) 4 – (–2) Substitute 6 for y 2, –3 for y 1, 4 for x 2, and –2 for x 1. = y 2 – y 1 x 2 – x = 3 2 = The slope of the line that passes through (–2, –3) and (4, 6) is. 3 2 *** Always reduce your fractions****

Understanding Slope Two (non-vertical) lines are parallel if and only if they have the same slope. (All vertical lines are parallel.)

Understanding Slope The slope of AB is: The slope of CD is: Since m 1 =m 2, AB || CD

Perpendicular Lines ( ┴ )Perpendicular Lines- 2 lines that intersect forming 4 right angles Right angle

Slopes of  Lines In a coordinate plane, 2 non vertical lines are  iff the product of their slopes is -1. This means, if 2 lines are  their slopes are opposite reciprocals of each other; such as ½ and -2. Vertical and horizontal lines are  to each other.

Example Line l passes through (0,3) and (3,1). Line m passes through (0,3) and (-4,-3). Are they  ? Slope of line l = Slope of line m = l  m Opposite Reciprocals!

Equation of a line in slope intercept form (y = mx+b) Now that we know how to find slope given any two points, we can generate an equation of the line connecting the two points. Example : points (3,2) and (6,9)

2 nd example

Slope-Intercept Form (y = mx+b) Find the equation of a line passing through the points P(0, 2) and Q(3, –2). Is this line parallel to a line with the equation

a) Find the equation of a line that passes through the points G ( -4, 5) and H (-8, 3) b) Write the equation of a line that passes through point P (1, -2) and is perpendicular to the one from part a

Slope Graphically You can always count ! (not suggested as you advance In your math courses)

Homework

Another application of Slope run rise Slope is rise run The steepness of the ramp matters to people who need to walk on it. or Rise:Run

No minimum pitch in the code. Required slope would be determined by roofing materials. Most shingle type roofs require minimum 4 in 12 pitch. You can go as low as 2.5 in 12 with special underlayment. Some local jurisdictions with heavy snowfall require a steep pitched roof for obvious reasons.

Rhode Island Code The Maximum slope for wheel chair ramps is 1:8.

The house has a platform 6 ft off the ground. If RI code says the maximum slope is 1:8 What could the lengths of the run be for a ramp?

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