1. 3.6A Lines in the coordinate plane (Writing & classifying equations)
Geometry

2. We’ve learned to graph given an equation.
Now we’ll learn to write the equation given the graph
There are three ways.
It all depends on what information you are given as to which process you use.

3. A.)Given the slope, m, and the y-intercept, b, use the equation y=mx+b
Ex. 1
The y-intercept is -3
b=-3
The slope is 4/3
The equation is:
y = x – 3 3 4

4. B.) If you are given slope, m, and a point (x1,y1) on the line Use Point Slope Form:
y – y1 = m ( x – x1)

5. Ex. 2 Write an equation of a line containing the point (1,2) with slope of -1/2.
Use (x1,y1) = (1,2) & m = -1/2
y – 2 = -1/2 ( x – 1)
Now you can simplify to the slope intercept form
y – 2 = -1/2 x + ½
y = -1/2 x + 5/2

6. C.) Given two points Use slope formula first.
Then, either use point-slope formula or slope-intercept form twice.

7. Ex. 3 Given two points (-2,2) & (3,7)
Find the slope:
m=1
Plug this slope and one of the points into the point slope formula.
y – 2 = 1 ( x – (-2))
y – 2 = x + 2
y = x (put the equation into slope intercept form)
(3,7)
(-2,2)

8. Classification of lines
Parallel lines have same slope with different y-intercept.
Intersecting lines have different slopes.
Coinciding lines have same slope & same y-intercept. (IMS)

9. Ex. 4 Determine whether the lines are parallel, intersect or coincide.
6x - 12y = -24, 3y = 2x + 18
intersect

10. 3-6B Writing equations of lines parallel or perp. Lines & graphs

11. Write equations of parallel or perpendicular lines
Ex. 1 Write an equation of the line that passes through (-2,1) and is
a.)parallel to y = -3x + 4

12. Ex. 1 Write an equation of the line that passes through (-2,1) and is
b.) perpendicular to y = -3x + 4

13. Ex. 2 Write a model using slope-intercept form
The number of U.S. cell phone subscribers increased from 16 million in 1993 to 44 million to Find the average rate of change and use it to estimate the number of subscribers in 1997.

14. Assignment

15. Ex. 6 Write a model using standard form
You have $6 to spend on drinks and a salad at the school cafeteria. The drinks cost $1.25 each and the salad costs $.20 per ounce. Write an equation that models this situation.
1.25x+.20y=6