NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3
Jan 11, 2016
NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3
Slope-Intercept FormSlope-Intercept Form(of a line)(of a line)
bmxy Where m is the slope (in the form of a fraction)
b is the y-intercept
x & y are points on the line in the form (x, y)
Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of –3.
Answer: The slope-intercept form of the equation of the line is
Slope-intercept form
Write an equation in slope-intercept form of the line with slope of –1 and y-intercept of 4.
Your Turn:
Point-Slope Form Point-Slope Form (of a line)(of a line)
)( 11 xxmyy Where:
And (x, y) never get replaced.
Answer:
Write an equation in point-slope form of the line
whose slope is that contains (–10, 8).
Simplify.
Point-slope form
Write an equation in point-slope form of the line
whose slope is that contains (6, –3).
Your Turn:
Write an equation in slope-intercept form for a line containing (4, 9) and (–2, 0).
Find the slope of the line.
Slope formula
Simplify.
Example 4-3bExample 4-3b
bmxy
b 49 23
b69
Now use the slope-intercept form and either point to write an equation.
Slope-intercept form
Fill in m & b.
Using (4, 9):
Solve for bb3
323 xy
OR Using (–2, 0):
Answer:
bmxy
b 20 23
b 30
Slope-intercept form
Fill in m & b.
Solve for bb3
323 xy
(–2, 0)
Write an equation in slope-intercept form for a line containing (3, 2) and (6, 8).
Answer:
Write an equation in slope-intercept form for a line containing (-2, 4) and (6, -2).
Answer:
Write an equation in slope-intercept form for a line containing (-2, 4) and (-2, -2).
Example 4-4aExample 4-4aWrite an equation in slope-intercept form for a line containing (1, 7) that is perpendicular to the line
the slope
of a line perpendicular to it is 2.
bmxy
b 127
b27
Slope-intercept form
Fill in m & b.
Solve for bb5
52 xy
)7 ,1( ,2m
Write an equation in slope-intercept form for a line containing (4, 1) that is perpendicular to the line
44 xy
Your turn:
Answer:
RENTAL COSTS An apartment complex charges $525 per month plus a $750 security deposit. Write an equation to represent the total annual cost A for r months of rent.
For each month of rent, the cost increases by $525. So the rate of change, or slope, is 525. The y-intercept is located where 0 months are rented, or $750.
Answer: The total annual cost can be represented by the equation
Slope-intercept form
RENTAL COSTS An apartment complex charges $525 per month plus a $750 security deposit. Compare this rental cost to a complex which charges a $200 security deposit but $600 per month for rent. If a person expects to stay in an apartment for one year, which complex offers the better rate?
First complex: Second complex:
Simplify.
Answer: The first complex offers the better rate: one year costs $7050 instead of $7400.
Answer:
RENTAL COSTS A car rental company charges $25 per day plus a $100 deposit.
a. Write an equation to represent the total cost C for d days of use.
b. Compare this rental cost to a company which charges a $50 deposit but $35 per day for use. If a person expects to rent a car for 9 days, which company offers the better rate?
Answer: The first company offers the better rate. Nine days cost $325 instead of $365.