1. 4 minutes
Warm-Up
1) Find the slope of the line containing the points (-1,12) and (5,-6).
2) Identify the slope and y-intercept for the line y = -5x + 7.
3) Write the equation in slope-intercept form for the line that has a y-intercept of 0 and a slope of -1.

2. 1.3.1 Linear Equations in Two Variables
Objectives:
Write a linear equation in two variables given sufficient information

3. Example 1
Write an equation for the line containing the points (1,5) and (2,8).

4. Example 1 y = mx + b 5 = 3 (1) + b 5 = 3 + b -3 -3 2 = b y = 3x + 2
Write an equation for the line containing the points (1,5) and (2,8).
y = mx + b
substitute 5 = 3
(1)
+ b
simplify
5 = 3 + b -3 -3
2 = b
y = 3x + 2

5. The Point-Slope Equation
y – y1 = m(x – x1)

6. Example 2
Write an equation for the line with slope 7 that contains the point (3,4).
y – y1 = m(x – x1)
y – 4 = 7(x – 3)
y – 4 = 7x - 21
y = 7x - 17

7. Example 3
Write an equation for the line containing (5,7) and (2,1).
First, find the slope:
y – y1 = m(x – x1)
y – 7 = 2(x – 5)
y – 7 = 2x - 10
y = 2x - 3

8. Example 4
Write an equation for the line shown below.
First, find any two points on the line.
(-3,-3)
and
(1,-1) 4 2 -4 -2 2 4
y – y1 = m(x – x1) -2 -4
y + 3 = ½(x + 3)
y + 3 = ½x + 1½
y = ½x – 1½

9. Example 5
Marva left her house and drove at a constant speed to a conference in another state. She picked up Delia along the way. Two hours after picking up Delia, they were 140 miles from Marva’s house, and 5 hours after picking up Delia, they were 344 miles from Marva’s house. How far from her house was Marva when she picked up Delia?

10. Homework
p.26 #11-31 odds

11. 4 minutes
Warm-Up
Write an equation for the line given the indicated points.
1) (-6,-6) and (-3,1)
Write an equation in point-slope form for the line that has the indicated slope, m, and contains the given point.
2) m = 4; (9,-3)

12. 1.3.2 Linear Equations in Two Variables
Objectives:
Write an equation for a line that is parallel or perpendicular to a given line

13. Activity
Graph y = 2x + 1.
On the same screen, graph y = 2x, y = 2x – 2.5, and y = 3x + 1.
Which equations have graphs that appear to be parallel to that of y = 2x + 1?
y = 2x, y = 2x – 2.5
What do these equations have in common?
same slopes
Write an equation in slope-intercept form for a line whose graph you think will be parallel to that of y = 2x Verify by graphing.

14. Activity Graph y = 2x + 1. On the same screen, graph
Which equations have graphs that appear to be perpendicular to that of y = 2x + 1?
What do these equations have in common?
their slopes are negative reciprocals of each other

15. Activity
Write an equation in slope-intercept form whose graph you think will be perpendicular to that of y = 2x Verify by graphing.

16. Parallel Lines
Parallel lines are lines in the same plane that never intersect.
Parallel lines have the same slope. -8 -6 -4 -2 2 4 6 8

17. Perpendicular Lines
Perpendicular lines are lines that intersect to form a 900 angle. -8 -6 -4 -2 2 4 6 8
The product of the slopes of perpendicular lines is -1.

18. Example 1 Determine whether these lines are parallel or perpendicular.
y – 2 = 5x + 4
and
-15x + 3y = 9
+15x x
y = 5x + 6
3y = x
y = 3 + 5x
y = 5x + 3
The lines have the same slope.
So they are parallel.

19. Example 2
Write an equation in slope-intercept form for the line containing (-3,-5) and parallel to the line y = 2x + 1.
m = 2
First, we need the slope of the line y = 2x + 1.
Second, we need to find out the slope of the line that is parallel to y = 2x + 1.
Lastly, we use the point-slope formula to find our equation.
y + 5 = 2x + 6
y = 2x + 1

20. Example 3
Write an equation for the line containing (-3,-5) and perpendicular to the line y = 2x + 1.
First, we need the slope of the line y = 2x + 1.
m = 2
Second, we need to find out the slope of the line that is perpendicular to y = 2x + 1.
Lastly, we use the point-slope formula to find our equation.

21. Homework
p.26 #35-51 odds