$\text { Find an equation of the line through the points of intersection of } y = x ^ { 2 } \text { and }$ $y = 6 x - x ^ { 2 }$
A) $y = x - 6$
B) $y = 6 x$
C) $y = - 6 x$
D) $y = 3 x$
E) $y = x + 3$

Question

Quizplus · Accepted Answer

The points of intersection are found by setting $x^2 = 6x - x^2$, which simplifies to $2x^2 - 6x = 0$. Solving gives $x = 0$ and $x = 3$. The points are $(0,0)$ and $(3,9)$. The slope of the line through these points is $\frac{9-0}{3-0} = 3$. Thus, the equation is $y = 3x$.

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$\text { Find an equation of the line through the points of intersection of } y = x ^ { 2 } \text { and }$