Question

Jae is a real estate photographer. The amount he earns in one week is a linear function of the number of houses he photographs.
If he photographs 2 houses, he earns $315, and if he photographs 7 houses, he earns $1015.
a. Create a linear model for Jae's earnings (y) (in dollars) as a function of the the number of houses he photographs (x), and put
the model in slope-intercept form.

Answer 1

  Equation of a linear function is defined by equation y = mx + b,

where m = slope of the line and b = y-intercept

  Linear model representing a function for the earning (y) to photograph the houses (x) will be,

y = 140x + 35

   Let the linear equation representing the earnings to photograph the houses,

y = mx + b

         If we graph a line with two variables, earnings from photography on y-axis and the number of houses at x-axis,

Slope of the line 'm' = $\frac{\triangle y}{\triangle x}$

     If two points lying on the line are (2, 315) and (7, 1015).

Slope of the line 'm' = $\frac{1015-315}{7-2}$

                                 = $\frac{700}{5}$

                                 = 140

     Therefore, equation of the line will be,

y = 140x + b

       Since, (2, 315) lies on the line,

315 = 140(2) + b

315 = 280 + b

b = 35

       Now the equation will be,

y = 140x + 35

        Therefore, linear model representing a function of the earning (y) to photograph the houses (x) will be,

y = 140x + 35

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