A computer technician charges $190 for a 3-hour appointment and $370 for a 7-hour appointment. Which of these represents a linear function that models the charge for hiring the technician for x hours? A y=55x+190 B y=55x+45 C y=45x+190 D y=45x+55

The linear function that models the charge for hiring the technician for x hours is y=45*x + 55

Step-by-step explanation:

The linear function is defined by the equation

f(x) = mx + b or y = mx + b

where m is the slope of the line and b is the y-intercept.

In this case you want to represent a linear function that models the charge for hiring the technician for x hours, that is, y represents the charge for hiring the technician and x the number of hours.

Given the coordinates of two points (x1, y1) and (x2, y2), you can determine the equation of the line first knowing the slope m by:

In this case, the points are:

So:

Solving:

m=45

To obtain the value of b, once you have replaced the value of m in the equation, you must substitute the values of x and y for the values of the coordinates of one of the points, and solve for b to obtain its value. In this case you replace the value of point 1:

And you get:

190= 135 + b

190 - 135= b

55= b

So, the linear function that models the charge for hiring the technician for x hours is y=45*x + 55

step-by-step explanation:

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