Writing Equations From A Table Worksheet Answer Key

WRITING AN EQUATION FROM A TABLE WORKSHEET

Problem 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.

Problem 2 :

A salesperson receives a weekly salary plus a commission for each computer sold. The table shows the total pay, y, and the number of computers sold, x. Write an equation in slope-intercept form to represent this situation.

Detailed Answer Key

Problem 1 :

Solution :

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 :

(x₁ , y₁ ) =(100, 14)

(x₂ , y₂ ) = (200, 20)

Then,

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

Substitute m = 0.06, and (x, y) = (100, 14).

14 = 0.06(100) + b

14 = 6 + b

8 = b

Step 4 :

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

y = mx + b

y = 0.06x + 8

Problem 2 :

Solution :

Step 1 :

Notice that the change in total pay is the same for increase in sales of every 2 computers . 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 (4, 550) and (6, 700).

Use the slope formula.

m = (y₂ - y₁) / (x₂ - x₁)

Substitute :

(x₁ , y₁ ) =(4, 550)

(x₂ , y₂ ) = (6, 700)

Then,

m = (700 - 550) / (6 - 4)

m = 150 / 2

m = 75

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

Substitute m = 75, and (x, y) = (4, 550).

550 = 75(4) + b

550 = 300 + b

250 = b

Step 4 :

Now, substitute m = 75 and b = 250 in slope-intercept form equation of a line.

y = mx + b

y = 75x + 250

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