The equation of a line in slope-intercept form, is given by:
[tex]y=mx+b[/tex]Where m represents the slope of the line, which is the rate of change of y with respect to x, and b represents the y-intercept of the line, which is the initial value of y when x=0.
If we use C to represent the vertical axis and p for the horizontal axis, then:
[tex]C=mp+b[/tex]From the data on the graph, we can see that C=200 when p=0. Then, the initial value is 200, then:
[tex]b=200[/tex]On the other hand, C=250 when p=1. Substitute this information in the equation to find the value of m:
[tex]\begin{gathered} C=mp+200 \\ \Rightarrow250=m(1)+200 \\ \Rightarrow m=50 \end{gathered}[/tex]Therefore:
[tex]C=50p+200[/tex]Since Sydney pays for the building and equipment regardless of the number of manufactured phones, then the initial value represents the rent of that building and equipment.
The y-intercept of the function is 200, which represents the rent of the building and equipment, or the cost of producing 0 phones.