Geometry
Section 3-3 Slopes of Lines
You will find the slope of lines by counting or by using the slope formula.
You will determine if two lines are parallel, perpendicular or neither by comparing their slopes.
The Slope of a Line
The steepness or slope of a hill is describes by the ratio of the hill’s vertical rise to its horizontal run.
On a graph you can count the rise over the run or use the formula.
Slope =
vetical change
horizontal change
=
rise y2 − y1
=
run x2 − x1
Find the slope of each line.
Ex 1.
Ex 2 .
Slope = m=
Slope = m =
Find the slope of the line for the following points
4. A(7, 6) and B(13, 16)
5. C(4, -3) and D(7, 6)
Ex 3.
Slope = m =
6. E(-4, 3) and F(-7, -12)
Slope can be interpreted as a rate of change, describing how the quantity y changes in relation to the quantity x
Slopes of Parallel Lines
If two lines are parallel then their slopes are equal.
Any two vertical lines are parallel and any two horizontal lines are parallel
Slopes of Perpendicular Lines
If two lines are perpendicular then the product of their slopes is -1 and their slopes are opposite reciprocals
of each other.
Any horizontal line and vertical line are perpendicular
Determine whether 𝑨𝑩 and 𝑪𝑫 are parallel, perpendicular, or neither.
8. A(14, 13), B(-11, 0) and C(-3, 7), D(-4, -5)
9. A(3, 6), B(-9, 2) and C(5, 4), D(2, 3)
10. A(8,-2), B(4, -1) and C(3,11), D(-2, -9)
Determine whether 𝑭𝑮 and 𝑯𝑱 are parallel, perpendicular, or neither for F(1, -3), G(-2, -1), H(5, 0), J(6, 3).
Graph each line to verify your answer.
y
6
5
4
3
2
1
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
x
–2
–3
–4
–5
–6
Assignment page 193: 12-33, 62, 64, 66, omit 27