Subjects algebra

Linear Function

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Linear Function


1. **State the problem:** We are asked to solve and analyze the function $y = -x + 5$. 2. **Rewrite the equation:** The function is a linear equation, where the slope is $-1$ and the y-intercept is $5$. 3. **Find the $y$-intercept:** Set $x=0$: $$y = -0 + 5 = 5$$ So, the graph crosses the y-axis at point $(0,5)$. 4. **Find the $x$-intercept:** Set $y=0$: $$0 = -x + 5 \\ x = 5$$ So, the graph crosses the x-axis at point $(5,0)$. 5. **Interpretation:** This is a straight line decreasing with slope $-1$, passing through points $(0,5)$ and $(5,0)$. **Final answer:** The function $y = -x + 5$ has $y$-intercept at $(0,5)$ and $x$-intercept at $(5,0)$. The slope is $-1$, indicating a line decreasing from left to right.