Question

find the value of f(7).
y = f(x)
answer attempt 1 out of 2

Explanation:

Step1: Find the equation of the right - hand line

The right - hand line passes through the points \((0,4)\) and \((4,0)\).
The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 4}{4 - 0}=- 1\).
Using the point - slope form \(y - y_1=m(x - x_1)\) with \((x_1,y_1)=(0,4)\), we get \(y-4=-1(x - 0)\), so \(y=-x + 4\).

Step2: Evaluate \(f(7)\)

Since \(x = 7\) lies on the right - hand line \(y=-x + 4\).
Substitute \(x = 7\) into \(y=-x + 4\), we have \(y=-7 + 4\).

Answer:

\(-3\)