Chapter 3: Parallel and Perpendicular Lines

3-6 Lines in the Coordinate Plane

Objectives: Student will be able:

1.To write the equations of lines in slope intercept form

2.To graph lines given their equation

HW/CW: pgs 169 #’s 2 – 16, 30-36 Even

Slope-Intercept Form

y = mx + b m is the slope

b is the y-interceptYou need m and b to write the

equation!

Write the equation of the line.What is the y-

intercept?b = -2What is m?

m = 3/2

y = 3/2x -2

x

y

Write the equation of the line.b = ?b = 1m = ?

m = -1/2

y = -1/2x + 1

x

y

Write the equation of the line.

b = ?b = 4m = ?m = 0 y = 4

x

y

Find the slope and y-int. of each equation.

1) y = -4x + 3

m = -4

b = 3

2) y = 5 - 1/2x

m = -1/2

b = 5

3) 8x + y = 3/4

m = -8

b = 3/4

4) 4x - 2y = 10

m = 2

b = -5

Type 1: Write the equation given the slope and y-intercept

1) m = -3, b = 1

y = -3x + 1

2) m = -2/5, b = -4

y = -2/5x - 4

x- and y-intercepts

● The x-intercept is the point where a line crosses the x-axis.

The general form of the x-intercept is (x, 0). The y-coordinate will always be zero.

● The y-intercept is the point where a line crosses the y-axis.

The general form of the y-intercept is (0, y). The x-coordinate will always be zero.

Finding the x-intercept

● For the equation 2x + y = 6, we know that y must equal 0. What must x equal?

● Plug in 0 for y and simplify.

2x + 0 = 6

2x = 6

x = 3

So (3, 0) is the x-intercept of the line.

Finding the y-intercept

● For the equation 2x + y = 6, we know that x must equal 0. What must y equal?

● Plug in 0 for x and simplify.

2(0) + y = 6

0+y = 6

y = 6● So (0, 6) is the y-intercept of the line.

To summarize….

●To find the x-intercept, plug in 0 for y.

●To find the y-intercept, plug in 0 for x.

Find the x- and y-interceptsof x = 4y - 5

● x-intercept:● Plug in y = 0

x = 4y-5

x = 4(0) - 5

x = 0 - 5

x = -5● (-5, 0) is the x-int.

● y-intercept:● Plug in x = 0

x = 4y-5

0 = 4y - 5

5 = 4y

5/4 = y● (0, 5/4) is the y-int.

Find the x- and y-interceptsof y = -3x – 1

● x-intercept● Plug in y=0

y = -3x - 1

0 = -3x - 1

1 = -3x

-1/3 = x● (-1/3, 0) is the x-int.

● y-intercept● Plug in x=0

y = -3(0) - 1

y = 0 - 1

y = -1● (0, -1) is the y-int.

Find the x- and y-intercepts of 6x - 3y =-18

● x-intercept● Plug in y=0

6x-3y=-18

6x-3(0) = -18

6x - 0 = -18

6x = -18

x = -3● (-3, 0) is the x-int.

● y-intercept● Plug in x=0

6x-3y=-18

6(0)-3y = -18

0 - 3y = -18

-3y = -18

y = 6● (0, 6) is the y-int.

Find the x- and y-intercepts of x=3

●y-intercept

●A vertical line never crosses the y-axis.

●There is no y-int.

●x-intercept

●Plug in y=0

●There is no y. Why?

●X=3 is a vertical line so x always equals 3.

●(3, 0) is the x-int.

x

y

Find the x- and y-intercepts of y=-2

●x-intercept

●Plug in y=0

●Y cannot = 0 because y=-2.

●y=-2 is a horizontal line so it never crosses the x-axis.

●There is no x-int.

●y-intercept

●Y=-2 is a horizontal line so y always equals -2.

●(0,-2) is the y-int.

x

y

Graphing Equations

● Example: Graph the equation -5x + y = 2

Solve for y first.

-5x+y=2 Add 5x to both sides.

y=5x+2

● The equation y=5x+2 is in slope-intercept form, y=mx+b. The y-intercept is 2 and the slope is 5. Graph the line on the coordinate plane.

x

y

1. Graph y=5x+2

●Example :Graph the equation 4x - 3y = 12.

● Solve for y first.

4x-3y=12 Subtract 4x from both sides.

-3y = -4x + 12 Divide by -3.

y = -4/-3 x+ 12/-3. Simplify.

y = 4/3 x – 4● The equation y=4/3 x - 4 is in slope-intercept form,

y=mx+b. The y-intercept is -4 and the slope is 4/3. Graph the line on the coordinate plane.

Graphing Equations

2. Graph y=4/3 x - 4

x

y