slope lesson 2-3 algebra 2. slope slope basically describes the steepness of a line if a line goes...
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SLOPELESSON 2-3
Algebra 2
Slope
Slope basically describes the steepness of a line
If a line goes up from left to right, then the slope has to be positive
Conversely, if a line goes down from left to right, then the slope has to be negative
Slope Formula
12
12
xx
yy
x
y
run
risemslope
In order to use that formula we need to know, or be able to find 2 points on the line
Procedure for Finding Slope
To find the slope given two points: Determine the values of x1,
x2, y1, and y2
Substitute the value of each variable in the formula and solve
Simplify the fraction as much as possible
DO NOT write the fraction as a mixed number of a decimal
12
12
xx
yym
(-3, 7) and (4, -6)
Examples of Finding Slope
(4, -1.5) & (3, 2.5) (1/2, 2/3) & (5/6, 1/4)
Horizontal & Vertical Lines
Horizontal lines have a slope of zero (when 0 is on top of a fraction)
Vertical lines have no slope (when 0 is under the fraction bar)
m = 0
m = no
slope
Your Turn:
Find the slope of the line passing through each pair of points. Then Graph the line.
1.(-1, 4) and (1, -2)
2.(-2, -3) and (0, -5)
3.(5, -4) and (5, 6)
4.(2, -7) and (-3, -7)
Graphing a Line Given a Point and Slope
To graph a line given a point on the line and the slope of the line: Plot the given point on
graph paper From that point, use your
slope to find another point on the line
Connect your points to draw the line
(-4, -3) and m = 2/3
12
12
xx
yym
More Graphing…
(2, -1) and m = 3 (-3, -4) and m = -3/2
More Graphing…
(1, 4) and m = 0 (-2, -1) and m = no slope
Your Turn…
Graph the line passing through the point (-3, -1) with m = -3
Standard Form and Slope
If a line is in the form Ax + By = C, we can use the following formula to find the slope:
B
Am
Examples of Finding Slope Given Standard Form
5x – 4y = 8 15x + 3y = 17
Parallel Lines & Slope
Parallel lines have the same slope.
Graph the line through (-1, 3) that is parallel to the line with equation x + 4y = -4.
Find the slope of the line with the given equation
Plot the point you are given
Use the slope you found to graph another point
Draw a line through the points
Your Turn…
Graph the line through (2, -1) that is parallel to the line with equation 2x + 3y = 6.
Perpendicular Lines & Slope
The slopes of perpendicular lines are opposite reciprocals.
What is a opposite reciprocal?
Perpendicular Lines & Slope
Graph the line through (4, -2) that is perpendicular to the line with equation 3x – 2y = 6.
Find the slope of the line with the given equation
Find the opposite reciprocal of this slope
Plot the point you are given Use the opposite reciprocal
slope you found to graph another point
Draw a line through the points
Your Turn…
Graph the line through (-1, 5) that is perpendicular to the line with equation 5x – 3y = 3.
Answer this question in your warm-up book.
How does slope apply to the steepness of roads?
Include the following in your answer:
•A few sentences explaining the relationship between the grade of a road (the amount a road rises divided by the horizontal distance of the road) and the slope of a line
•A graph of y = 0.1x which corresponds to a 10% grade (The scale on your x- and y-axes should be the same.)
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