2003 AMC 10B Problems/Problem 11

Problem

A line with slope $3$ intersects a line with slope $5$ at point $(10,15)$ . What is the distance between the $x$ -intercepts of these two lines?

$\textbf{(A) } 2 \qquad\textbf{(B) } 5 \qquad\textbf{(C) } 7 \qquad\textbf{(D) } 12 \qquad\textbf{(E) } 20$

Using the point-slope formula, the equation of each line is

$y-15=3(x-10) \longrightarrow y=3x-15\\ y-15=5(x-10) \longrightarrow y=5x-35$

Substitute in $y=0$ to find the $x$ -intercepts.

\[0=3x-15\longrightarrowx=5
0=5x-35\longrightarrowx=7\] (Error compiling LaTeX. Unknown error_msg)

The difference between them is $7-5=\boxed{\textbf{(A) \ } 2}$ .

2003 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
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