Question

Write the point-slope form of an equation to find the total fee y for any number of hours x.

a) y - 195 = 15(x - 9)
b) y = 15x + 195
c) y = 9x + 15
d) y - 9 = 15(x - 195)

Answer 1

The correct point-slope form of the equation to find the total fee y for any number of hours x, based on the provided example of Svetlana's tutoring charge, is y - 25 = 15(x), where 25 is the y-intercept and 15 is the slope. So, the correct answer is a) y - 195 = 15(x - 9).

Step-by-step explanation:

The question is asking for the point-slope form of an equation to find the total fee y for any number of hours x.

Given the provided examples, where Svetlana charges a one-time fee plus either hourly or session fees, we can derive that the general form should include both a slope, which represents the rate per hour, and a y-intercept, representing the initial fee.

For instance, in Example 12.4, where Svetlana tutors to earn extra money, the equation given is y = 25 + 15x, with a slope of 15 and a y-intercept of 25.

Converting this equation into the point-slope form, since the y-intercept is given when x = 0, we would have the point-slope form as y - 25 = 15(x - 0).

Thus the correct equation for Svetlana's tutoring service in point-slope form would be: y - 25 = 15(x).

So, the correct answer is a) y - 195 = 15(x - 9).