SLOPE of A LINE

Slope• What is slope?• Why do we want to know?• Look at the relationship between rise and run in each of the lines. That would define the slope of the line.

X

y

Look at the relationship between the blue arrow and the red arrow

Line 1

Line 2

Line 1 Line 2

=

Rise (↕)

Run (↔)

Difference in the y coordinate

Difference in the x coordinate

1

2

What is the slope of this staircases?

- 1

2

SLOPE

Practice Problems

#1

#2

#3

Draw three different staircases that have a slope of 3/2. Label the riser and runner for each staircase.

What is the slope of this staircase?

What is the slope of this line?

A B

CHALLENGE PROBLEM:

Draw a line with a slope of 3/1. Can you draw more than 1?

Slope Practice

A B

Order these staircases from flattest to steepest (#1 is the flattest, #2 is the next flattest). If two staircases have the same slope, give them the same number.

A B C D

E F G

{ F, C, E, A/D, G, B }

{ .4, .666, .75, 1/1, 1.666, 4 }

Special cases

Horizontal Line

m= 0

Vertical Line

m = undefined

Finding the slope given two points

Find the slope of the line that passes through (2, 3) and (4, -1)

Two ways to do this:a) With a pictureb) With a formula

Two ways:a) Do it on a graphb) Formula: m = y2-y1

x2-x1

Find the slope through (3, 2) and (-1, 5)

Find the slope of the lines that contain the following

points

a) (1, 0) and (-2, 1)

a) (2, 3) and (5, -2)

a) (3, 3) and (1, -1)

The slope is the coefficient of x (you might have to solve for y first)

Find the slope of the these equations:

a) y = -2x + 1 m =

b) 3y + 2x = -9 m =

c) x - y = 4 m =

Equations of lines in slope intercept formy = mx + b

m = slope is the number next to x (the coefficient of x)

b = the y-intercept (the point where the lines crosses the y-axis)

Find the slope and the y-intercept

€

y =3

5x + 2

y = 2x −2

y = x

m y-int

To graph using the slope and y-intercept

1) Start on the y-axis at b

2) Use the slope m to draw the triangle (you need a fraction here)

• Positive m - up and right • Negative m - down and right

€

y =2

3x − 4

y = 3x +1

y = −x

Use the slope and y-intercept to graph lines

€

2x + y = 3

Drawing a Line with One Point & The Slope

Draw the line that passes through (-1, -3) & has Slope = 4/2

Example #2. Point (-4, 3) & Slope = -3/2

Slope: slope m =

1. To find slope from two points: use the formula or draw the two points and draw the

triangle.

2.To find slope from a graph: draw the triangle (you need to choose two points on the line first)

3.To find slope from an equation - solve for y first, the slope is the coefficient of x.

Parallel Lines: they have the same slopePerpendicular Lines - slopes and opposites and reciprocals from each other

€

rise

run

Sketching Lines

To sketch a line you need to know:

A) direction: given by the sign of m

B) steepness: given by the absolute value of m

C) where it hits the y-axis: given by b

Pos neg

Sketch and describe the line

y = 2x - 1 3x + 2y = 4

x = -2 y = 0 y = -5x€

y =1

3x + 2

Parallel lines

Have the same slope.

Are these lines parallel?a) You need the slope mb) You might have to solve for y

first.

Perpendicular Lines

Triangles I drew to find slope

They are the same - just rotatedThe run of the first is the ____of the second one.The rise of the first is the ____of the second one.

If the slope of the first one is mThe slope of the second one is_____

1) Are the following lines perpendicular, parallel or neither?

y = 3x + 2 and y = -3x + 4y = 3x + 2 and y = 1/3 x + 2y = 3x + 2 and y = -1/3 x + 2y = 3x + 2 and y = 3x - 5

2) Find the slope of the line perpendicular and parallel to the graph of each line:

y = 3/2 x + 7y = 12x + y = 3y = 3x - 2