Lesson 5-4 Point

```Lesson 5-4
Point-Slope Form
Sept. 22, 2014
Daily Learning Target
• I will write and graph linear
equations using point-slope
form.
What is it?
y – y1 = m(x – x1)
m = slope
(x1, y1) = a point the line
goes through.
Here is how it works!!
• Given a point (x1, y1) on a line and the
line’s slope m, you can use the definition
of slope to derive point-slope form.
y2 – y1
• Definition of slope (m) =
x2 – x1
• Let (x, y) be any point on the line.
Substitute for (x, y) for (x2, y2).
y – y1
•
=m
x – x1
How it works cont.
y – y1
•
=m
x – x1
• Multiply both sides by x – x1
y – y1 = m(x – x1 )  point-slope form
m = slope
(x1, y1) = a point the line goes through.
Example 1
• A line passes through (-3, 6) and has slope -5.
What is an equation of the line in point slope
form?
**Remember: y – y1 = m(x – x1 )
y – 6 = -5(x + 3 )
You Try It
2
.
3
• A line passes through (8, -4) and has slope
What is an equation in point-slope for of the
line?
y+4=
2
(x
3
– 8)
Example 2
• What is the graph
of the equation
y–1=
2
(x
3
– 2)
What is the slope?
What is the point
it passes through?
You Try
• What is the graph
of the equation:
a. y + 7 = -
4
(x
5
– 4)
b. y – 1 = -3(x + 2)
c. y – 2 =
4
(x
9
– 3)
Example 3
• What is an equation of the line from the
coordinate plane?
Steps to think about:
• Think  --You need the slope m, so start with
the slope formula.
– Use the given points to find the slope
– Use point-slope form
– Use either point for (x1, y1).
You Try
• Use the same procedure as the example to
write the equation for a graph where the line
goes through points (-3, 4) and (1, 1).
y–1=-
3
(x
4
– 1)
Example 4
• The table shows the altitude of a hot-air
balloon during its linear descent. What
equation in point-slope form. What does it
look like in slope-intercept form?
• PSF: y – 640 = -2.5(x – 10)
• SIF: y = -2.5x + 665
Time, x (s)
Altitude, y (m)
10
640
30
590
70
490
90
440
You Try
• The table shows the number of gallons of
water, y, in a tank after x hours. The
relationship is linear. What is an equation in
point-slope forms that models that data.
What does the slope
Time, x (h)
Water, y (gal)
represent?
2
3320
PSF: y – 3320 = 1250(x – 2);
3
4570
The rate at which water is
5
7070
8
10,820
being added to the tank.
Homework
• Workbook:
• Page 151 problems 1, 3, 4, 6, 7, 8, 10, 11, 13
• Page 153 problems 1-6 ALL
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