+164 What is the equation of the reflection of the line y = 2x + 1 across the line y = 5x - 3? Give your answer in slope-intercept form.
+15079 The equation of the reflection of the line y = 2x + 1 across the line y = 5x - 3.
Intersection:
\(f_1(x)=f_2(x)\\ 2x+1=5x-3\\ 3x=4\\ x_{1,2}=\frac{4}{3}\\ y_{1,2}=\frac{11}{3}=3\frac{2}{3}\\ P_{1,2}(1\frac{1}{3},3\frac{2}{3})\)
gradient
\(m_{1,2}=tan\ [\frac{1}{2}(\arctan 2+\arctan 5)]\\ m_{1,2}=2.9145\)
Point direction equation
\(y=m(x-x_P)+y_P \\ y=2.914536(x-1.\overline {33})+3.\overline{66}\\ y=2.914536x-3.886053+3.666667 \)
The equation of the reflection is
\(\color{blue}f_{1,2}(x)= y=2.914536x-0.219381\)
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