Question

Steven earns extra money babysitting he charges $33 for 4 hours and $57.75 for 7 hours entering an equation to represent the relationship let x represent the number of hours Stephen babysits and let y represent the amount he charges the equation is y = ​

Answer 1

y = 8.25x

Explanation:

Linear Modeling

Some events can be modeled as linear functions. If a situation comes where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The linear function can be expressed in the slope-intercept format:

`y=mx+b`

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

`\displaystyle y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Let's use linear modeling to represent Steven's earnings he makes babysitting. Call y the money he charges by x hours of work.

We know he charges y1=$33 for x1=4 hours, and y2=$57.75 for x2=7 hours. The ordered pairs are (4,33) and ( 7, 57.75)

Computing the equation of the line we have:

`\displaystyle y-33=(57.75-33)/(7-4)(x-4)`

Operating:

`\displaystyle y-33=(24.75)/(3)(x-4)`

`y - 33 = 8.25( x - 4 )`

`y = 8.25x - 33 + 33`

y = 8.25x

There is a proportional relationship.