Write an equation in point-slope form of the line that passes through the given ^ See Problem 4.
points. Then write the equation in slope-intercept form.- (1 ,4), (-1 ,1 ) 20. (2, 4), ( - 3 , - 6 ) 21. ( - 6 , 6), (3, 3)
Model the data in each table with a linear equation in slope-intercept form.
Then tell what the slope and y-intercept represent.
(^256)
3 44
(^520)
23.
25.50
Q Apply Graph the line that passes through the given point and has the given slope m.
- (-3, -2); m = 2 25. (6, - 1 ) ; m = - § 26. (-3,1); m = |
2 7. T h ink A b o u t a Plan The relationship of degrees Fahrenheit (°F) an d degrees Celsius
(°C) is linear. W hen the tem perature is 50°F, it is 10°C. W hen the tem perature is
77°F, it is 25°C. Write an equation giving the Celsius tem perature C in term s of the
Fahrenheit temperature F. W hat is the Celsius tem perature w hen it is 59°F?
- How can point-slope form help you write th e equation?
- W hat are two points you can use to find th e slope?
I 28. a. Geom etry Figure ABCD is a rectangle. W rite eq u atio n s in point-slope
form of th e lines containing th e sides of ABCD.
b. Reasoning Make a conjecture a b o u t th e slopes of parallel lines.
c. Use your conjecture to write an eq u a tio n of th e line th a t passes
through (0, - 4 ) an d is parallel to y - 9 = —7(x + 3).
^221 29. Boiling Point The relationship b etw e en altitude an d th e boiling p o in t
of w ater is linear. At a n altitude of 8000 ft, w ater boils at 197.6°F. At an
altitude of 4500 ft, w ater boils at 203.9°F. W rite a n eq u a tio n giving the
boiling point b of water, in degrees F ahrenheit, in term s of the altitude a,
in feet. W hat is the boiling p o in t of w ater at 2500 ft?
- W hat are two points you can use to find th e slope?
- Using a graphing calculator, graph / ( x ) = 3x + 2.
a. If /(x ) = 3x + 2 an d g(x) = 4/(x), write th e eq u a tio n for g(x). G raph g(x) and
com pare it to th e g raph o f/(x ).
b. If /(x ) = 3x + 2 an d h{x) = / ( 4x), w rite th e eq u a tio n for h(x). Graph h{x) and
com pare it to th e g raph o f/(x ).
c. C om pare how m ultiplying a function by a n u m b e r an d m ultiplying th e x value of
a function by a n u m b e r change th e graphs of th e functions. - Using a graphing calculator, graph / ( x ) = 2x - 5.
a. If /(x) = 2x - 5 and j(x) = J\x) + 3, write th e eq u a tio n for j{x). Graph j(x) and
com pare it to th e graph o f/(x ).
b. If /(x ) = 2x - 5 a n d k(x) = / ( x + 3), w rite th e eq u a tio n for k[x). Graph k(x) and
com pare it to th e graph o f/(x ).
c. C om pare how adding a n u m b e r to a function a n d adding a n u m b e r to th e x
value of a function change th e graphs of th e functions.
I Lesson 5-4 Point-Slope Form
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