Question

the table below provides the amount of savings y generated after saving money for x weeks use the table below to answer the following questions A) Below is a copy of a students work finding the liner equation that models the given data describe the error in the students work of finding the liner equation B) correctly find the liner equation in slope intercept form that models the given data

Answer 1

A)

Consider that the slope 'm' of the line, representing the relationship between 'y' and 'x', is given by the formula,

`m=(y_2-y_1)/(x_2-x_1)`

As observed, the student applied the formula between the points (3,350) and (5,450) but the student made a mistake in the denominator.

Mistake: The student took (3-5) in the denominator which is wrong as per the numerator. He/she should take (5-3) in the denominator.

And the correct slope will be calculated as,

`\begin{gathered} m=(450-350)/(5-3) \\ m=(100)/(2) \\ m=50 \end{gathered}`

B)

Let the linear model representing the relation between 'y' and 'x' be,

`y=mx+b`

Substitute the value of the slope,

`y=50x+b`

Pick any of the given pair of values (x,y) from the table.

Since the equation of line is the model for all the given data, coordinates of each point must satisfy the linear equation. This logic can be used to obtain the value of unknown variable 'b'.

Let us take the point (7,550) to obtain the value of 'b' as follows,

`\begin{gathered} 550=50(7)+b \\ 550=350+b \\ b=550-350 \\ b=200 \end{gathered}`

Substitute the value back in the linear equation,

`y=50x+200`

Thus, the required linear equation is obtained as,

`y=50x+200`