1.4 Graphing Lines

If real is what you can feel, smell, taste, and see, then “real” is simply electrical signals interpreted by the brain.

-Morpheus

Slope of a Line

x

y

x2 x1

y2 y1

P2(x2,y2)

P1(x1, y1)

m y2 y1

x2 x1

x1 x2

Slope of a Line

x

y

P2(11,6)

P1(2,3)

m y2 y1

x2 x1

x1 x2

Slope of a LineFind the slope of the line shown below.

Vertical and Horizontal LinesLet’s take a look at the vertical line and horizontal line through the point (-3,1).

Vertical Lines

Slope Undefined

x aEquation:

y b

Horizontal Lines

Slope = 0Equation:

Forms of a Line

y mx bSlope-Intercept Form:

y y1 m(x x1)Point-Slope Form:

Ax By CGeneral Form:

m = slope b = y-intercept

m = slope (x1,y1) = point on line

A,B are integers ≠ 0 and A > 0

Ex : y 12

x 3

Ex : y 3 12

(x 0)

Ex : y 2 12

(x 2)

Ex : x 2y 6

Forms of a Line - Practice1) Write the equation of the line in general form.

y 23

x 4

2) Write the equation of the line in slope-intercept form.

(y 2) 12

(x 1)

Finding Equations From GraphsFind the equation of the line. Write your answer in slope-intercept form.

Finding the Equation of a LineFind an equation for the line with the given properties. Express your answer in Slope-Intercept Form.

1) Slope = 2; containing the point (4,-3)

Finding the Equation of a LineFind an equation for the line with the given properties. Express your answer in General Form.

2) Containing the points (-3,4) and (2,5)

Finding the Equation of a LineFind an equation for the line with the given properties.

3) Slope undefined containing the point (3,8)

Parallel and Perpendicular Lines

Parallel Lines have slopes that are equal.

Perpendicular Lines have slopes that are opposite reciprocals.

Finding the Equation of a LineFind an equation for the line with the given properties. Express your answer in Slope-Intercept Form.

4) Parallel to the line 3x + y = 4; containing the point (-1,2)

Finding the Equation of a LineFind an equation for the line with the given properties. Express your answer in General Form.

5) Perpendicular to the line x - 2y = -5; containing the point (0,4)

Graphing Lines in General FormWhen equations are in general form, we can use the intercepts to help us graph without solving for y.

2x 4y 8

More Practice…before you get your homework, k?

1) Find the slope of the line containing the points (-2,-1) and (5,-6).

2) Find the slope and the y-intercept of the following lines.

2x 5y 10

(y 4) 34

(x 8)

3) Find the equation of the line below in slope-intercept form.

a) b)

1.4 Graphing Lines

If real is what you can feel, smell, taste, and see, then “real” is simply electrical signals interpreted by the brain.

-Morpheus

Homework #14:Graphing Worksheet