Find R Ccc5D8

1. **State the problem:** We are given two functions: $$g(x) = f(rx)$$ and $$f(x) = -3x + 5$$. We need to find the value of $$r$$ such that the graph of $$g(x)$$ matches the given description. 2. **Understand the functions:** Since $$g(x) = f(rx)$$, substituting $$f(x)$$ gives: $$g(x) = -3(rx) + 5 = -3r x + 5$$ 3. **Analyze the graphs:** Both lines cross the y-axis at about 5, which matches the constant term 5 in both functions. 4. **Find the x-intercepts:** - For $$f(x) = -3x + 5$$, set $$f(x) = 0$$: $$0 = -3x + 5$$ $$3x = 5$$ $$x = \frac{5}{3}$$ - For $$g(x) = -3r x + 5$$, set $$g(x) = 0$$: $$0 = -3r x + 5$$ $$3r x = 5$$ $$x = \frac{5}{3r}$$ 5. **Use the graph information:** The red line $$g(x)$$ crosses the x-axis at about 5, so: $$\frac{5}{3r} = 5$$ 6. **Solve for $$r$$:** $$\frac{5}{3r} = 5$$ Multiply both sides by $$3r$$: $$5 = 5 \times 3r$$ $$5 = 15r$$ Divide both sides by 15: $$r = \frac{5}{15}$$ Simplify the fraction: $$r = \frac{1}{3}$$ **Final answer:** $$r = \frac{1}{3}$$