Q:

PLS help!!!Which scenario best matches the linear relationship shown in the table?Weeks Dollars0 102 204 306 40a. Shanna had $10 in her piggy bank and earned $10 each week in allowance.b. Shanna had $10 in her piggy bank and earned $5 each week in allowance.c. Shanna had $10 in her piggy bank and spent $5 each week on stickers.d. Shanna earns $10 each week.

Accepted Solution

A:
The scenario that "Shanna had $10 in her piggy bank and earned $5 each week in allowance" best matches the given linear relationship.What is linear equation in two variable?An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b and c are real numbers and the coefficients of x and y, i.e. a and b respectively, are not equal to zero. What is linear relationship?A linear relationship creates a straight line when plotted on a graph.The linear relationship can be expressed as a mathematical equation of the  form y = mx +b.Let x represents the number of weeks and y represents the dollar earned.And the linear equation which represent this scenario is y = mx + b According to the given question In the starting  of week Shanna had $10.⇒ 10 = m × 0 + b   (  at initially, when x = 0)⇒ b = 10 In the second week Shanna had $20⇒ 20 = m(2) + 10                    (  because, b =10)⇒ 10 = 2m ⇒ m = 5Therefore, the equation which represents this linear relationship is y = 5x + 10        ( because, m = 5 and b = 10)⇒ Shanna had $10 in her piggy bank and earned $5 each week in allowance. Hence, the option b is correct.Learn more about linear relationship here: