Show that the graph of the inverse of f(x)=mx+b, where m and b are constants and m≠0, is a line with slope 1/m and y-intercept -b/m.

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Start with the given function: $f(x) = mx + b$, where $m$ and $b$ are constants and $m \neq 0$.

To find the inverse function $f^{-1}(x)$, replace $f(x)$ with $y$: $y = mx + b$.

Swap the roles of $x$ and $y$ to find the inverse: $x = my + b$.

Solve this equation for $y$ to express the inverse function: subtract $b$ from both sides to get $x - b = my$, then divide both sides by $m$ to isolate $y$: $y = \frac{x - b}{m}$.

Rewrite the inverse function in slope-intercept form: $f^{-1}(x) = \frac{1}{m}x - \frac{b}{m}$. This shows the inverse is a line with slope $\frac{1}{m}$ and $y$-intercept $-\frac{b}{m}$.

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