The true statement about the graph of f(x) is [tex]f(x) = \frac 35x + 3[/tex]
The graph of f(x) is a straight line that passes through the points (-5,0) and (0,3).
Start by calculating the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{3-0}{0--5}[/tex]
Simplify
[tex]m = \frac{3}{5}[/tex]
The equation of the line is then calculated as:
[tex]y = m(x -x_1) + y_1[/tex]
This gives
[tex]y = \frac 35(x -0) + 3[/tex]
Open bracket
[tex]y = \frac 35x + 3[/tex]
Express y as a function of x
[tex]f(x) = \frac 35x + 3[/tex]
Hence, the true statement about the graph of f(x) is [tex]f(x) = \frac 35x + 3[/tex]
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