Question

Luna's savings increases as a linear function of the number of chores she does, as shown in the table. » How much money did Luna have saved before she started doing chores? Chores Savings ($) 74 1 2 78 3 82 4 86 $68 $70 $64 $0 10

Answer 1

we are given a chart of values and we are told they increase linearly. We will first find the equation for the line that describes the chart. we will find first the slope of the line using the points (1,74) and (2,78), using the following formula

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

replacing the values

`m=(78-74)/(2-1)=4`

the general equation for the line is

`y=mx+b`

the value b, we find it using the point (1,74), replacing we get

`74=4(1)+b`
`\begin{gathered} 74-4=b \\ 70=b \end{gathered}`

the equation for this line is

`y=4x+70`

Since "x" represents the chore, when we set x = 0 in the equation of the line, we get the value of the savings, that is, y = 70