Dr. Fowler CCM Slope - Harder

WRITE NOTES: The steepness of the roof of a house is referred to as the pitch of the roof by home builders. Give one reason why some homes have roofs which have a greater pitch? There is less snow build up in the wintertime.

3 m 5 m Determine the slope (pitch) of the roof.

Engineers refer to the slope of a road as the grade. They often refer to the slope as a percentage.

Rise = 8 Run = 100 A grade of 8% would mean a rise of 8 units, for every run of 100 units = 8% The slope of a line is the steepness of the line.

y = mx + b. m = slope b = y-intercept Given an equation of a line, find the slope and y-intercept.

3x + 5y = 10 Solve for y: 1) subtract 3x 5y = -3x + 10 y = -3 x + 2 m = slope = -3/5b = y intercept = 2 Example: Find the slope and y-intercept: -3x __ 2) Divide by 5 __ __ 5 Now solved for y and in slope-intercept form

If a linear equation is solved for y, the coefficient of the x represents the slope of the line. Solve for y to find slope:

Parallel Lines are two or more lines with the same slope. These two lines are parallel. Parallel Lines

Perpendicular Lines exist if the product of their slopes is –1. These two lines are perpendicular. Perpendicular Lines: -2x+5y = -3

Write an equation of a line given the slope and the y-intercept. Equations of Lines

The slope of a line that goes through the points (r, 6) and (4, 2) is 4. Find r. To solve this, plug the given information into the formula

To solve for r, simplify and write as a proportion. Cross multiply. 1(-4) = 4(4 – r)

Simplify and solve the equation. 1(-4) = 4(4 – r) -4 = 16 – 4r = -4r -4 5 = r The ordered pairs are (5, 6) and (4, 2)

The End

Excellent Job !!! Well Done

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