1. Section P.4…slope, forms of equations of lines, parallel and perpendicular lines, + applications!

2. Definition: Slope of a Line
The slope of the nonvertical line through the points
(x , y ) and (x , y ) is 1 1 2 2
y – y y 2 1
m = = x
x – x 2 1
If the line is vertical, then x = x , and the slope
is undefined. 1 2

3. Forms of Equations of Lines
General Form:
Ax + By + C = 0
(A and B integers, A>0, )
y = mx + b
Slope-Intercept Form:
y – y = m(x – x )
Point-Slope Form: 1 1
Vertical Line:
x = a
Horizontal Line:
y = b

4. Guided Practice Find the slope of the line through the pair of points.
(–1, 2) and (4, –2)
(–9, –3) and (9, 25) 4 14 –
m =
m = 5 9

5. Guided Practice
Find the value of x or y so that the line through the
pair of points has the given slope.
(–2, 7) and (x, –2), m = 3
Equation for slope:
x = –5

6. Guided Practice
Find the equation of the line through (–3, –4) with slope 2.
 Use point-slope form  we love it!!!
Rewrite in slope-intercept form:
y = 2x + 2

7. Guided Practice: Find a general form equation for the line through
the pair of points (–3, –8) and (4, –1).
First, find slope:
Next, point-slope form:
Re-write to general form:

8. Guided Practice:
Find the x- and y-intercepts of the following equation
using your grapher:
436x + 9y = 1298
Solve for y:
Graph window???
Calculate answers:

9. More guided practice! 3x – 2y = 14
Find the value of x and the value of y for which (x, 14) and
(18, y) are points on the graph.
3x – 2y = 14
Substitute first point:
Substitute second point:
Complete points: (14, 14) and (18, 20)

10. Parallel and Perpendicular Lines
1. Two nonvertical lines are parallel if and only if
their slopes are equal.
2. Two non-vertical lines are perpendicular if and only
if (iff) their slopes m and m are opposite
reciprocals. That is, iff 1 2 1
m = 1 m 2

11. (–2, 3) y = –2x + 4 Parallel Line Perpendicular Line
Find an equation for the line passing through the point that is
parallel to the given line and an equation through the given
point that is perpendicular to the given line.
(–2, 3)
y = –2x + 4
Parallel Line
Perpendicular Line
Point:
Slope:
Point:
Slope:
Point-Slope Form:
Point-Slope Form:

12. Guided Practice: y = –2000x + 50,000
A corporation purchased a $50,000 building and depreciates it
$2000 per year over a 25-year period.
1. Write a linear equation giving the value of y of the building
in terms of the years x after the purchase.
y = –2000x + 50,000
2. In how many years will the value of the building be
$24,500?
Solve this three ways – algebraically, graphically, and using a table!

13. Whiteboard Practice:
Determine a and b so that the figure PROC is a parallelogram.
R(a,b)
O(8,5)
P(1,0)
C(6,0)

14. Homework: p. 40-43 3-25 odd, 41, 43, 55, 57 Whiteboard Practice:
Find the equation of the line through the points
(4, 2) and (–3, 1). Write your answer in slope-
intercept form. 1 10
y = x + 7 7
Homework: p odd, 41, 43, 55, 57