Answer
a) For the Links phone company
y = 60x
For Connections phone company
y = 40x + 300
b) It will take Links phone company 15 months to get to a cost of 900.
It will also take Connections phone company 15 months to get to a cost of 900.
c) Check Explanation
Step-by-step explanation
a) The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
For the Links phone company
m = slope = 60
b = y-intercept = 0
y = mx + b
y = 60x + 0
y = 60x
For Connections phone company
m = slope = 40
b = y-intercept = 300
y = mx + b
y = 40x + 300
y = 40x + 300
b) The question asks us to write an equation to find how many months it will take each company will take to get to a total cost of 900
For Links phone company
y = 60x
we now need to solve for x given that y = 900
y = 60x
900 = 60x
We can rewrite this as
60x = 900
Divide both sides by 60
(60x/60) = (900/60)
x = 15 months
For Connections phone company
y = 40x + 300
we now need to solve for x given that y = 900
y = 40x + 300
900 = 40x + 300
Subtract 300 from both sides
900 - 300 = 40x + 300 - 300
600 = 40x
We can rewrite this as
40x = 600
Divide both sides by 40
(40x/40) = (600/40)
x = 15 months
c) For the Links phone company
y = 60x
For Connections phone company
y = 40x + 300
y = 60x
y = 40x + 300
We will try to solve this by equating the two equations to get when the two companies will have the same total cost
60x = 40x + 300
60x - 40x = 300
20x = 300
Divide both sides by 20
(20x/20) = (300/20)
x = 15 months
For Links phone company
when x = 15 months
y = 60x = 60 (15) = 900
For Connections phone company
when x = 15 months
y = 40x + 300
y = 40 (15) + 300
y = 600 + 300
y = 900
Hope this Helps!!!