Question

Help with writing equations.The pictures below have the questions I need help with.

Answer 1

I'm sure you know how to find the slope of a line if you know 2 points
on it ...  The slope is ...

       (difference in y-values) / (difference in x-values) .

Right ?

OK.  Each line in these tables is a point on the graph of the table.
Pick two points from the table, and you can get the slope of the line
from them.

The first table (Plan-A) has these points in it:

1 . . . . . $20.15
2 . . . . . $20.30
3 . . . . . $20.45
4 . . . . . $20.60

You want to find the equation of the line with these 4 points on it.
That means you need to find the slope and the intercept of the line.
Take any two points straight from the table.  I'll use the first two:

1 . . . . . $20.15
2 . . . . . $20.30

There you have two points on the line:  (1, 20.15) and (2, 20.30) .
The slope is  (difference in 'y') / (difference in 'x').

Difference in 'y' = (20.30 - 20.15) = 0.15
Difference in 'x' = (2 - 1) = 1

Slope of the line =  (0.15) / 1  =  0.15
(What that really means is 15 cents per minute on Plan-A.)

Now you know that the equation of the line is [ y = 0.15x + intercept ].

Can you think of a way to find the intercept ?
Remember ... every point in the table is on the line.
So why not just take one of these points in the table, put it into the part of the equation that you already have, and watch the intercept fall out ?
You could use any point at all from the table.
I'll use the 3rd one.

                                                         y = 0.15x + intercept

                                                  20.45 = 0.15(3) + intercept

                                                  20.45 = 0.45 + intercept

Subtract 0.45 from each side:    20.00 = intercept

The equation of the graph for Plan-A is    Charge = 0.15(minutes) + $20.00
===============================

Plan-B:

First two points:

Difference in y-values = (8.00 - 6.50) = 1.50
Difference in x-values = (10 - 5) = 5

Slope of the line = (1.50) / (5) = .30                (30 cents per minute)
Intercept = 5.00

Charge = 0.3(minutes) + $5.00
======================================

Plan-C:

Slope = 4.50 / 10  =  0.45
Intercept = zero
=================================

Plan-D:

Slope = (16.50 - 11.00) / (30 - 20) = 5.5/10 = 0.55
Intercept = zero

In each plan, the intercept is the cost just to sign up, before you use
the phone, and then the slope is the cost for each minute of talking on it.