Answer:
<em>y = 8.25x</em>
Step-by-step explanation:
<u>Linear Modeling</u>
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:

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

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:

Operating:



y = 8.25x
There is a proportional relationship.
Answer:
To find why he would do this, we need to understand what all the possible first steps are in this equation.
You could add 4 to both sides.
You could subtract 4 from both sides.
You could subtract 5x from both sides.
You could subtract 6x from both sides.
Any of these work. In Bernard's case, he added 5 negative x tiles, meaning he subtracted. C and D already make no sense, but allow me to further explain. By him subtracting 5x from both sides, the equation turns into:
-4 = x + 4
By this point, he can just subtract 4 from both sides to find the value of x. But the question asks for why he did the first step. Therefore, it would

The value of the discriminant is
12.
Since the discriminant is greater than zero, the equation has
two real solutions.