Properties of Intersecting Lines

Since $L_1$ passes through $(5,8)$, $8 = k(5-1) \implies 4k = 8 \implies k = 2$. So line $L_1$ is $y = 2(x - 1) = 2x - 2$. Line $L_2$ has slope 1 and passes through $(5,8)$, so $y - 8 = 1(x - 5) \implies y = x + 3$.

• $y$-intercept of $L_1$ is $(0, -2)$.
• $y$-intercept of $L_2$ is $(0, 3)$. Distance between y-intercepts = $3 - (-2) = 5$. Therefore, option A ("The distance between the y-intercepts of the two lines is 6") is definitely FALSE.