Questions: The slope of the line passing through points (x1, y1) and (x2, y2) is found using the formula (y2-y1)/(x2-x1). The line passing through the points (1,2) and (x, 5) is perpendicular to a line that has a slope of 1/3. What is the value of x ? A 10 B -2 C -4 D 0

The slope of the line passing through points (x1, y1) and (x2, y2) is found using the formula (y2-y1)/(x2-x1). The line passing through the points (1,2) and (x, 5) is perpendicular to a line that has a slope of 1/3. What is the value of x ? A 10 B -2 C -4 D 0
Transcript text: The slope of the line passing through points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ is found using the formula $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$. The 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 $x$ ? A 10 B -2 C -4 D 0
failed

Solution

failed
failed

Solution Steps

To find the value of \( x \), we need to determine the slope of the line passing through the points \((1, 2)\) and \((x, 5)\). Since this line is perpendicular to a line with a slope of \(\frac{1}{3}\), its slope must be the negative reciprocal, which is \(-3\). We set up the equation for the slope \(\frac{5 - 2}{x - 1} = -3\) and solve for \( x \).

Step 1: Determine the Slope of the Perpendicular Line

The line passing through the points \((1, 2)\) and \((x, 5)\) is perpendicular to a line with a slope of \(\frac{1}{3}\). Therefore, the slope of our line must be the negative reciprocal of \(\frac{1}{3}\), which is \(-3\).

Step 2: Set Up the Slope Equation

The slope of the line through the points \((1, 2)\) and \((x, 5)\) is given by the formula: \[ \frac{5 - 2}{x - 1} = -3 \]

Step 3: Solve for \( x \)

Simplify and solve the equation: \[ \frac{3}{x - 1} = -3 \] Multiply both sides by \((x - 1)\) to eliminate the fraction: \[ 3 = -3(x - 1) \] Distribute the \(-3\): \[ 3 = -3x + 3 \] Subtract 3 from both sides: \[ 0 = -3x \] Divide by \(-3\): \[ x = 0 \]

Final Answer

The value of \( x \) is \(\boxed{0}\).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Some new laptops come with an L3 with a capacity of up to 8 MB . Cache Printer Hard drive Bandwidth
failedAnswered
Figure 2-4 shows various points on three different production possibilities frontiers for a nation. Refer to Figure 2-4. A movement from Y to Z represents an increase in the demand for plastic products, is the result of advancements in plastic production technology, is the result of advancements in food production technology, is the result of a decrease in preference for food products.
failedAnswered
Write the fraction in lowest terms. 30/50
failedAnswered
Select the correct answer. A civil engineer is designing a public parking lot for the new town hall. The number of cars in each row should be six less than the number of rows in the lot. The mayor has requested that the new lot should hold twice as many cars as the current parking lot, which has space for 56 cars. Determine which equation the civil engineer can use to find the number of rows, x, he should include in the new parking lot. A. x^2 - 6x = 112 B. 2x^2 - 12x = 112 C. x^2 - 6 = 112 D. 6x^2 - 56 = 112
failedAnswered
The volume of a cone with height h and radius r can be found using the formula V=1/3 π r^2 h Find the volume of a cone with radius 7 feet and height 4 feet. ft^3