the slope of the line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is found using the formula…

the slope of the line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is found using the formula $\\frac{y_2 - y_1}{x_2 - x_1}$.\n\nthe line passing through the points $(1, 2)$ and $(x, 5)$ is perpendicular to a line that has a slope of $\\frac{1}{3}$. what is the value of $x$?\n\na 10\nb -2\nc -4\nd 0

the slope of the line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is found using the formula $\\frac{y_2 - y_1}{x_2 - x_1}$.\n\nthe line passing through the points $(1, 2)$ and $(x, 5)$ is perpendicular to a line that has a slope of $\\frac{1}{3}$. what is the value of $x$?\n\na 10\nb -2\nc -4\nd 0

Answer

Explanation:

Step1: Identify the perpendicular slope

The slope of a perpendicular line is the negative reciprocal. $$m = -\frac{1}{1/3} = -3$$

Step2: Set up the slope equation

Use the given points $(1, 2)$ and $(x, 5)$. $$\frac{5 - 2}{x - 1} = -3$$

Step3: Simplify the numerator

Calculate the difference in $y$-values. $$\frac{3}{x - 1} = -3$$

Step4: Solve for $x$

Multiply both sides by $(x - 1)$ and divide by $-3$. $$3 = -3(x - 1) \implies -1 = x - 1 \implies x = 0$$

Answer:

D. 0