1. Unit #3 Writing Equations of Lines

2. Slope Review
Slope formula

3. Find the slope between the points
(-4, 3) & (2, 10)

4. Find the slope between the points
(-2, 3) & (-2, 8)

5. Find the slope between the points
(8, 3) & (-2, 3)

6. Find the value of r so the line that passes through each pair of points has the given slope.
(1, r) & (4, -3) m = 2/3

7. Find the value of r so the line that passes through each pair of points has the given slope.
(2, 5) & (r, 6) m = -4

9. Equations of Lines Slope- intercept form y=mx+b mslope b y-intercept
y-int is where line crosses the y axis
y = -3x -2
slope is -3 (down 3 to the right 1)
y-int is -2 (line crosses y-axis at -2)

10. Practice slope intercept form
Write the equation of the line b=7 m= -1/2

11. Practice slope intercept form
Write the equation of the line y-int= 3 (-2, 3) (4, 1)

12. Practice slope intercept form
Write the equation of the line (0,2) (-2, 3)

13. Point-Slope Form
For a given point (x1, y1) on a non-vertical line with slope m, the point-slope form of a linear equation is as follows:
y – y1 = m(x – x1)
In general, you can write an equation in point-slope form for the graph of any non-vertical line. If you know the slope of a line and the coordinates of one point on the line, you can write an equation of the line. End in slope-intercept form unless otherwise stated.

14. Steps to follow Step 1: find slope (NEVER MAKE SLOPE A DECIMAL)
Step 2: plug x1, y1, and m into point-slope formula
Step 3: Distribute in the slope on right side of equation (NEVER MAKE SLOPE A DECIMAL)
Step 4: add/subtract y1 to the last number on the right side of the equation.

15. Ex. 1: Write the point-slope form of an equation of the line passing through (2, -4) and having a slope of 2/3

16. Practice point-slope form

17. Practice point-slope form
(2,-1) (-2, 0)

18. Practice point-slope form
(1, 3) (-2, -2)

20. Parallel and Perpendicular
Write the equation of the line parallel to y = -3x + 7 and passes through the point (3, 5)

21. Parallel and Perpendicular
Write the equation of the line parallel to y = 1/2x + 3 and passes through the point (0, 5)

22. Parallel and Perpendicular
Write the equation of the line perpendicular to y = 1/2x + 8 and passes through the point (1, -4)

23. Parallel and Perpendicular
Write the equation of the line perpendicular to y = x + 4 and passes through the point (-3, 0)

24. Parallel and Perpendicular
Write the equation of the line perpendicular to y = 5 and passes through the point (3, 2)

26. Standard Form
Any linear equation can be expressed in the form Ax + By = C where A, B, and C are integers and A and B are not both zero. This is called standard form. An equation that is written in point-slope form can be written in standard form.
Rules for Standard Form:
Standard form is Ax + By = C, with the following conditions: 1) No fractions 2) A is not negative (it can be zero, but it can't be negative). By the way, "integer" means no fractions, no decimals. Just clean whole numbers (or their negatives).

27. Going from Standard Form to Slope intercept
Rules: Step 1: subtract Ax from both sides put Ax right after = sign Step 2: divide ALL numbers by B

28. Example
3x + 4y = 12

29. Go from Slope-intercept form into standard form
Rules:
Step 1: add/subtract mx to both sides
Step 2: multiply every number by -1 if m is negative (not necessary every time)
Step 3: multiply every number by the slope’s denominator if it is a fraction (not necessary every time)

30. Example
y = -1/2x + 2

31. Example 2
y = 2/3x – 4