Question

1. find the value of f(x)=7.

Explanation:

Step1: Find the equation of the line

From the graph, the line passes through \((0, 4)\) (y - intercept, \(b = 4\)) and \((4, 0)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 4}{4 - 0}=\frac{- 4}{4}=- 1\). So the equation of the line is \(y=-x + 4\) (since \(f(x)=y\)).

Step2: Solve for \(x\) when \(f(x) = 7\)

Set \(y = 7\) in the equation \(y=-x + 4\). We get \(7=-x + 4\).
Subtract 4 from both sides: \(7-4=-x+4 - 4\), which simplifies to \(3=-x\).
Multiply both sides by - 1: \(x=-3\).

Answer:

The value of \(x\) when \(f(x) = 7\) is \(-3\).