slope the slope of a line (m) is the ratio of the vertical change (rise) to the horizontal change...

Slope

The SLOPE of a line (m) is the ratio of the vertical change (rise) to the horizontal change (run) between any 2 points.

Diagram & Symbol

Slope between 2 points

1. Find 2 points (x, y) that are on the line.

2. Use the slope formula to solve for m:

12

12

xx

yy

Slope-intercept form

An equation of a NON-vertical line:

𝒚=𝒎𝒙+𝒃Slope value

y-intercept value

PRACTICE!!!

Write the slope-intercept form of the equation for:slope = 3, y-intercept = 6slope = ½ , y-intercept = -5slope = -2/3 , y-intercept = 10

Point-Slope form

An equation of a non-vertical line with the value of a point & a slope value is:

)( 11 xxmyy

Slope value y-coordinate x-coordinate

PRACTICE!!!

Write the point-slope form of the equation for:Slope=2/3, goes through (-2, -6)Slope=-3, goes through (4, -1)Slope=7/12, goes through (5, -8)

How to write the point-slope equation between 2 points

1. Find the slope between the 2 points

2. Use the point-slope form to find the line

3. Write the new equation!

12

12

xx

yym

)( 11 xxmyy

Horizontal & Vertical Lines

Horizontal: y=1 (any number)

Vertical: x=1 (any number)

)5(7

41

)5(4

)3(3

13

xy

xy

xy

How to graph a slope-intercept equation

1. Plot the y-intercept point (0, y)

2. Count up/down the rise

3. Count left/right the run

4. Repeat for 2 additional points.

5. Connect the points with a line.

6

2

43

12

1

2

x

y

xy

xy

xy

Find the slope of line b

Find the slope of line a

Slope directions