# 2006 iTest Problems/Problem 5

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## Problem

A line has y-intercept $(0,3)$ and forms a right angle to the line $2x + y = 3$. Find the x-intercept of the line. $\mathrm{(A)}\,(4,0)\quad\mathrm{(B)}\,(6,0)\quad\mathrm{(C)}\,(-4,0)\quad\mathrm{(D)}\,(-6,0)\quad\mathrm{(E)}\,\text{none of the above}$

## Solution

The given line's equation is $y = -2x + 3$. Since the wanted line forms a right angle to the given line, the slopes of the two lines multiply to $-1$, so the slope of the wanted line is $\tfrac12$. Thus, the equation of the wanted line is $y = \tfrac12 x + 3$.

To find the x-intercept of the line, substitute $0$ for $y$ and solve for $x$. \begin{align*} \tfrac12 x + 3 &= 0 \\ \tfrac12 x &= -3 \\ x &= -6 \end{align*} The x-intercept of that line is $\boxed{\textbf{(D)}\,(-6,0)}$.

## See Also

 2006 iTest (Problems) Preceded by:Problem 4 Followed by:Problem 6 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • U1 • U2 • U3 • U4 • U5 • U6 • U7 • U8 • U9 • U10
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