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

21

step-by-step explanation:

11279

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.