Answer:
y = 8.25x
Step-by-step 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:
[tex]y=mx+b[/tex]
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
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:
[tex]\displaystyle y-33=\frac{57.75-33}{7-4}(x-4)[/tex]
Operating:
[tex]\displaystyle y-33=\frac{24.75}{3}(x-4)[/tex]
[tex]y - 33 = 8.25( x - 4 )[/tex]
[tex]y = 8.25x - 33 + 33[/tex]
y = 8.25x
There is a proportional relationship.
