1. Distance Formula and Writing Linear Equations

2. Linear Equations
Distance Formula.

3. Linear Equations Find the distance between the given points.
1) (3, 6) and (1, 2)
2) (-3, 4) and (2, -3)

4. Linear Equations Find the distance between the given points.
3) (-3, -1) and (1, 2)
4) (-3, -7) and (6, -3)

5. Linear Equations
Whenever the directions ask you to write the equation of the line, you will want to use the slope-intercept formula:
The parameters are “m” and “b”. The variables are “x” and “y”. For each problem, you will need to find the parameters. The variables will remain in your final answers.

6. Linear Equations
Ex. 1: Write the equation of the line that has m = 2 and passes thru the point (3, 4).

7. Linear Equations
Ex. 2: Write the equation of the line that has m = -4 and passes thru the point (-1, -2).

8. Linear Equations
Ex. 3: Write the equation of the line that has m = ½ and passes thru the point (-4, 5).

9. Linear Equations
Ex. 4: Write the equation of the line that has m = -2/3 and passes thru the point (6, 1).

10. Linear Equations
Ex. 5: Write the equation of the line that passes thru the points (6, 1) and (2, -3).

11. Linear Equations
Ex. 6: Write the equation of the line that passes thru the points (4, -1) and (2, -2).

12. Linear Equations
Ex. 7: Write the equation of the line that passes thru the points (5, -1) and (5, -6).
If the slope comes out undefined or zero, that means the equations are special cases.
According to HOY VUX, an undefined slope has x=# as the equation.
What does x=?

13. Linear Equations
Ex. 8: Write the equation of the line that has m= 2 and x-intercept = 3.

14. Linear Equations
Ex. 9: Write the equation of the line that is parallel to y = 3x + 5 and passes thru (4, -2).
If our line is supposed to be parallel to y = 3x + 5, we just need to know the slope because parallel lines have the same slope. What is the slope of the other line?

15. Linear Equations
Ex. 10: Write the equation of the line that is perpendicular to y = 2x – 4 and passes thru (4, -3).
Perpendicular slopes are negative reciprocals. That means, if you know one slope, flip it and change the sign to get the other.
What is the slope of the other line?

16. Linear Equations
Ex. 11: Write the equation of the line that is parallel to 2x – 3y = 5 and passes thru (-6, -1).

17. Linear Equations
Ex. 12: Write the equation of the line that is perpendicular to 3x + 4y = 8 and passes thru (-9, 2).

18. Linear Equations
Ex. 13: Write the equation of the line that is parallel to y = 2 and passes thru (-1, 3).
What kind of line is y=2?
What kind of lines are parallel to horizontal lines?
What do the equations of horizontal lines look like?
What does y = ?

19. Linear Equations
Ex. 14: Write the equation of the line that is perpendicular to y = 8 and passes thru (-5, -2).
What kind of line is y=8?
What kind of lines are perpendicular to horizontal lines?
What do the equations of vertical lines look like?
What does x = ?

20. Linear Equations
Now, you try it! Get with the same groups to work on the worksheet. The answers are at the bottom, so to get credit for your homework, you have to do more than just write the answers. I need to see your work.

21. Practice:
Write the equation of the line that passes thru the point (3, 4) and has the x-int = 5.
Write the equation of the line that is parallel to 3x – 4y = 8 and passes thru the point (-4, 2).
Write the equation of the line that is perpendicular to 3x + 4y = 8 and passes thru (-9, -2).
Write the equation of the line that passes thru the point (3, 4) and has slope = 2/3.
Find the distance between the points (3, -4) and (0, 0).

22. Warmup #3:
Write the equation of the line that passes thru the points (3, 4) and (0, -2).
Write the equation of the line that passes thru the point (-8, 4) and has slope = -3/4.
Find the distance between the points (-5, 1) and (3, -5).