1. Chapter 3: Parallel and Perpendicular Lines
3-6 Lines in the Coordinate Plane

2. 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, Even

3. Slope-Intercept Form
y = mx + b m is the slope
b is the y-intercept
You need m and b to write the equation!

4. Write the equation of the line.
What is the y-intercept?
b = -2
What is m?
m = 3/2
y = 3/2x -2 x y

5. Write the equation of the line.
b = ?
b = 1
m = ?
m = -1/2
y = -1/2x + 1 x y

6. Write the equation of the line.
b = ?
b = 4
m = ?
m = 0
y = 4 x y

7. 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

8. 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

9. 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.

10. 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.

11. 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.

12. To summarize…. To find the x-intercept, plug in 0 for y.
To find the y-intercept, plug in 0 for x.

13. Find the x- and y-intercepts of 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.

14. Find the x- and y-intercepts of 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.

15. 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.

16. Find the x- and y-intercepts of x=3
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.
y-intercept
A vertical line never crosses the y-axis.
There is no y-int. x y

17. 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

18. 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.

19. 1. Graph y=5x+2 x y

20. Example :Graph the equation 4x - 3y = 12.
Graphing Equations
Example :Graph the equation 4x - 3y = 12.
Solve for y first.
4x-3y=12 Subtract 4x from both sides.
-3y = -4x 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.

21. 2. Graph y=4/3 x - 4 x y