More math problems?

Question

1. The price of a 2-hour plumbing repair job is $130 and the price of a 5-hour job is $250. Find the slope of the line. Match your result to the correct answer below.
A) $50/hr B) $180/hr C) $40/hr D) $120/hr

2.The price of a 2-hour plumbing repair job is $130 and the price of a 5-hour job is $250. Write an equation for the cost of a t-hour repair job and use the equation to find the cost of a repair job lasting 6 hours.
A) C = 50t + 40; $340
B) C = 40t + 50; $290
C) C = 40t; $240
D) C = 40t + 40; $280

Thank you for any help that you can give.

Answer 1

Both questions are simple linear algebra. They all relate to the equation for a straight line (y = mx+b).
For Question 1:
Your are given two points on the line and asked to find the gradient. this can be easily found by dividing the different in the rise by the difference in the run. ie gradient = rise/run.
m = (y2-y1)/(x2/x1) = ($250-$130)/(5 hrs - 2hrs)
m = $120/3hrs = $40/hr
Therefore answer is C).

For Question 2:
Since the points given are the same as Q1 you already have the gradient. To obtain the equation of the line you need to find out the y- intercept (b), you can use either point to determine b:
y = mx + b
$130 = $40*2 + b
b = $50
Therefore the equation of the line is y = 40t + 50
to work out the cost for a 6 hr job, then substitute in 6 into the equation:
y = 40(6)+50
y = $290
Therefore answer B

Answer 2

if $ is y axis and time is x axis,
slope = change in y / change in x = change in $ / change in time
slope =[ 250-130] / [5-2]
slope = 120 / 3 = $ 40 / hr
Answer C


general equation:

C = slope (t) + a fixed cost
Pick a point and plug it in:
130 = 40 (2) + Fixed cost
fixed cost = 130-80 = 50
So:
C = 40t + 50 is the general equation.
and 6 hrs would cost:

C= 40(6) + 50
C = 240 + 50 = $ 290
Answer B

Answer 3

1.
plot 'cost' on 'y-axis' and 'hrs' on 'x-axis' as all ans are in /hr

now,
slope=(y2-y1)/(x2-x1)

hence,
slope(m) = 120/3 = 40

2.
now,
equation of this job is equation of line which is y=(m*x)+c

here,
when x = 5, y= 250

hence,
c= 50

therefore
equation is C = 40t + 50

and when t = 6
C = 40 * 6 + 50 = 290

Answer 4

your points are (2,130) and (5,250)
slope is (250-130)/(5-2)
=120/3=40 Choice C

Y=mx+b
y=40x+b
130=40(2)+b
b=50
y=40x+50 for 6 hrs C=290
Choice B