Question

A straight line $L_1$ has the equation $y = k(x - 1)$, where $k$ is some real number. The straight line $L_1$ intersects another straight line $L_2$ at the point $(5, 8)$. If $L_2$ has a slope of 1, which of the following is definitely FALSE?

Accepted Answer

A. Line $L_1$ passes through $(5,8) \implies 8 = k(5 - 1) \implies k = 2$. Equation of $L_1$: $y = 2(x - 1) \implies 2x - y - 2 = 0$. Line $L_2$ has slope 1 and passes through $(5,8) \implies y - 8 = 1(x - 5) \implies y = x + 3 \implies x - y + 3 = 0$. y-intercept of $L_1$ is $(0, -2)$ and y-intercept of $L_2$ is $(0, 3)$. Distance between y-intercepts = $3 - (-2) = 5$. Therefore, the statement claiming the distance between the y-intercepts is 6 is definitely FALSE.

Properties of Intersecting Lines

Explanation

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