Question

Three lines $k_1, k_2, k_3$ represent three different equations as shown in the figure below. Solution of the equations represented by lines $k_1$ and $k_3$ is $x = 3, y = 0$, while solution of equations represented by lines $k_2$ and $k_3$ is $x = 4, y = 1$. Which of the following is the equation of line $k_3$ ? (A) $x - y = 3$ (C) $x + y = 3$ (B) $x - y = -3$ (D) $x + y = 1$

Accepted Answer

A. Line $k_3$ passes through $(3, 0)$ and $(4, 1)$. Let the equation of line $k_3$ be $y - y_1 = m(x - x_1)$. First, calculate the slope $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 0}{4 - 3} = \frac{1}{1} = 1$. Using point $(3, 0)$ and slope $m=1$: $y - 0 = 1(x - 3)$ $y = x - 3$ $x - y = 3$ Let's check with point $(4, 1)$: $4 - 1 = 3$. This is correct.

Equation of a Line from Graph

Explanation

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