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Writing an Equation From a Desk Worksheet



Downside 1 :

Elizabeth’s mobile phone plan lets her select what number of minutes are included every month. The desk exhibits the plan’s month-to-month price y for a given quantity of included minutes x. Write an equation in slope-intercept kind to symbolize the state of affairs.

Downside 2 :

A salesman receives a weekly wage plus a fee for every laptop bought. The desk exhibits the entire pay, y, and the quantity of computer systems bought, x. Write an equation in slope-intercept kind to symbolize this case.

Solutions

Downside 1 :

Elizabeth’s mobile phone plan lets her select what number of minutes are included every month. The desk exhibits the plan’s month-to-month price y for a given quantity of included minutes x. Write an equation in slope-intercept kind to symbolize the state of affairs.

Resolution :

Step 1 : 

Discover that the change in price is similar for every enhance of 100 minutes. So, the connection is linear.

Step 2 : 

Select any two factors within the kind (x, y), from the desk to seek out the slope :

For instance, allow us to select (100, 14) and (200, 20).

Use the slope components. 

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 : 

Discover the y-intercept utilizing the slope and any level from the desk.

Slope-intercept kind 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 kind equation of a line.

y  =  mx + b

y  =  0.06x + 8

Downside 2 :

A salesman receives a weekly wage plus a fee for every laptop bought. The desk exhibits the entire pay, y, and the quantity of computer systems bought, x. Write an equation in slope-intercept kind to symbolize this case.

Resolution :

Step 1 : 

Discover that the change in whole pay is similar for enhance in gross sales of each 2 computer systems. So, the connection is linear.

Step 2 : 

Select any two factors within the kind (x, y), from the desk to seek out the slope :

For instance, allow us to select (4, 550) and (6, 700).

Use the slope components. 

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 : 

Discover the y-intercept utilizing the slope and any level from the desk.

Slope-intercept kind 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 kind equation of a line.

y  =  mx + b

y  =  75x + 250

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