Question

A line contains the points (−5, 1) and (1, k). It is also perpendicular to the line with equation 3x − 5y = 2. Find the value of k.

Answer 1

To find the value of k, we need to determine the slope of the given line and then use the fact that perpendicular lines have slopes that are negative reciprocals of each other.

Step-by-step explanation:

To find the value of k, we need to determine the slope of the given line and then use the fact that perpendicular lines have slopes that are negative reciprocals of each other.

First, we can find the slope of the given line by rearranging the equation 3x - 5y = 2 into slope-intercept form: y = (3/5)x - (2/5). The slope of this line is 3/5.

Since the line we are interested in is perpendicular to this line, its slope will be the negative reciprocal of 3/5. The negative reciprocal of 3/5 is -5/3.

Now, we can use the slope of -5/3 and the point (1, k) to find the value of k. Using the formula for the slope of a line, we have (-5/3) = (k - 1) / (1 - (-5)). Solving for k, we get k = -8.