Download 5.3 Objective: Point-Slope Form: Examples: Using Point

5.3
Objective:
Point-Slope Form:
Examples:

Using Point-Slope Form write an equation for a line with a slope of ½ that goes through (7, -2).

Write an equation in point-slope form of the line that passes through the point (4, –3) and has a
slope of 2.

Write an equation in point-slope form of the line that passes through the point (–1, 4) and has a
slope of –2.
Graphing Point-Slope Form:
Method 1: Change the signs on x1 and y1 then plot the point. Use the slope to find the next point.
Method 2: Solve for y by distributing and adding y1. This puts it in y = mx + b form.
Examples:


Graph: y + 2 = ⅔(x – 3)
o
Method 1:
o
Method 2:
Graph:
o
y – 1 = -(x – 2)
Method 1:
o
Method 2:

Graph y + 4 = 3(x – 1)

Graph y – 1 = ½(x + 2)
Writing an Equation in Point-Slope Form Given Two Points:
o
o
Find slope
Plug either point in. There are two possible answers, but they are identical if changed to y=mx+b
form.
Examples:

Write an equation in point-slope form that goes through the points (-1, 3) and (1, 1)

Write an equation in point slope form that goes through (-2, 3) and (1, -3)

Write an equation in point-slope form of the line that passes through the points (2, 3) and
(4, 4).
Problem Solving
Example 4: You are designing a sticker to advertise your band. A company charges $225 for the first
1000 stickers and $80 for each additional 1000 stickers. Write an equation that gives the total cost (in
dollars) of stickers as a function of the number (in thousands) of stickers ordered. Find the cost of 9000
stickers.
Extra Example: A radio station charges $650 for the first minute of ad time and then $340 for each
additional minute. Write an equation that gives the total cost (in dollars) to run an ad as a function of
the number of minutes the ad runs. Find the cost of 7 minutes of ad time.
How to tell if a situation is linear:
Example 5: The table shows the cost of visiting a working ranch for one day and night for different
numbers of people. Can the situation be modeled by a linear equation? Explain. If possible, write an
equation that gives the cost as a function of the number of people in the group.
Extra Example: The table shows the cost of renting a canoe for different times (in hours). Can the
situation be modeled by a linear equation? Explain. If possible, write an equation that gives the cost as a
function of time (in hours).
Time (hrs)
2
4
6
8
10
Cost ($)
22
32
42
52
62
Guided Practice #5 top of page 305:
•
Homework: 1, 2 – 12 ev, 14 – 19, 20 – 34 ev, 38 – 42ev, Bonus: 35, 36, 44