Arithemic sequerce
A car rental company charges a flat fee of $25 plus $0.15 per mile driven.
a) Write a linear function C(x) that represents the total cost C of renting the car after driving x miles. b) Use your function to find the total cost of driving 120 miles.
a) Writing the function
The total cost is made of, A flat fee: 25 A cost per mile: 0.15x
So the linear function is: C(x) = 25 + 0.15x
b) Plug in 120 miles
C(120) = 25 + 0.15(120) C(120) = 25 + 18 C(120) = $43
Line m has a slope of 3. Line n is parallel to line m and passes through the point (2, 5). Write the equation of line n.
Parallel lines have the same slope, so slope = 3. Use point‑slope form,
y − 5 = 3(x − 2)
y − 5 = 3x − 6
y = 3x − 1
A gym charges a $10 sign‑up fee plus $8 per month.
a) Write a linear function G(m) that represents the total cost after m months.
b) Find the total cost after 6 months.
a) G(m) = 10 + 8m
b) G(6) = 10 + 8(6) = 10 + 48 = $58
Line k is given by the equation y = −4x + 7. Write the equation of a line parallel to line k that passes through (0, −2).
Parallel → same slope = −4 Use point‑slope form:
y + 2 = −4(x − 0)
y + 2 = −4x
y = −4x − 2
A taxi company charges $3 to start the ride plus $2.25 per mile.
a) Write a linear function T(x) that represents the total cost for x miles.
b) How much does a 9‑mile ride cost?
a) T(x) = 3 + 2.25x
b) T(9) = 3 + 2.25(9) = 3 + 20.25 = $23.25
A line passes through the points (1, 3) and (4, 9). Write the equation of a line parallel to it that passes through (−2, 1).
m = (9 − 3) / (4 − 1) = 6 / 3 = 2 Parallel slope = 2 Use point‑slope form,
y − 1 = 2(x + 2)
y − 1 = 2x + 4
y = 2x + 5
A video game store gives you $5 for trading in a game plus $1.50 for each accessory you trade in.
a) Write a linear function V(a) that represents the total money you earn for a accessories.
b) How much do you earn if you trade in 7 accessories?
a) V(a) = 5 + 1.50a
b) V(7) = 5 + 1.50(7) = 5 + 10.50 = $15.50
Line p has the equation 3x − y = 12. Write the equation of a line parallel to line p that passes through (3, 0).
Rewrite in slope‑intercept form: 3x − y = 12 → −y = −3x + 12 → y = 3x − 12 Slope = 3 Use point‑slope form:
y − 0 = 3(x − 3)
y = 3x − 9
y = 3x − 9
A streaming service charges a $4 setup fee plus $6 per month.
a) Write a linear function S(m) that represents the total cost after m months.
b) How much will the service cost after 10 months?
a) S(m) = 4 + 6m
b) S(10) = 4 + 6(10) S(10) = 4 + 60 S(10) = $64
A line has slope 1/2 and y‑intercept 4. Write the equation of a line parallel to it that passes through (6, 1).
Parallel → same slope = 1/2 Use point‑slope form:
y − 1 = ½(x − 6)
y − 1 = ½x − 3
y = ½x − 2