How to write a equation using a table

Example 1 :  Elizabeth’s cell phone plan lets her choose how many minutes are included each month. The table shows the plan’s monthly cost y for a given number of included minutes x. Write an equation in slope-intercept form to represent the situation.

Step 1 :  Notice that the change in cost is the same for each increase of 100 minutes. So, the relationship is linear.

Step 2 :  Choose any two points in the form (x, y), from the table to find the slope :

For example, let us choose (100, 14) and (200, 20).

Use the slope formula.

m  =  (y2 - y1) / (x2 - x1)

Substitute (100, 14) for (x1, y1) and (200, 20) for (x2, y2).

m  =  (20 - 14) / (200 - 100)

m  =  6 / 100

m  =  0.06

Step 3 :

Find the y-intercept using the slope and any point from the table.

Slope-intercept form equation of a line :

y  =  mx + b

Plug m  =  0.06, and (x, y)  =  (100, 14)

14  =  0.06(100) + b

14  =  6 + b

8  =  b

Step 4 :

Now, plug m = 0.06 and b = 8 in slope-intercept form equation of a line.

y  =  mx + b

y  =  0.06x + 8

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

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