ANSWER
B. f(x) = 3x - 8
EXPLANATION
We have the graph of a straight line given and we need to find the function that it represents.
A linear function is generally given as:
f(x) = mx + c
where m = slope
c = y intercept
So, we need to identify the slope and y intercept.
The y intercept is the point where the graph touches the y axis. From the graph, the y intercept is:
c = -8
Now, to find the slope, we use the formula:
[tex]m\text{ = }\frac{y2\text{ - y1}}{x2\text{ - x1}}[/tex]
where (x1, y1) and (x2, y2) are two points that lie on the graph.
Let us use the given points:
(0, -8) and (1, -5)
Therefore:
[tex]\begin{gathered} m\text{ = }\frac{-5\text{ - (-8)}}{1\text{ - 0}}\text{ = }\frac{-5\text{ + 8}}{1} \\ m\text{ = 3} \end{gathered}[/tex]
Therefore, the equation of the line is:
f(x) = 3x - 8
