Question

What is the equation of the line in point-slope form that passes through the point (1, 2) and is perpendicular to the line 4x−6y=18?

A. y−2=23(x−1)
B. y−2=−23(x−1)
C. y+2=23(x−1)
D. y+2=−23(x−1)

Answer 1

To find the equation of a line perpendicular to another line, determine the slope of the given line and take its negative reciprocal. Then, use the point-slope form of the equation to write the equation of the new line.

Step-by-step explanation:

To find the equation of a line that is perpendicular to another line, we first need to determine the slope of the given line. The given line is of the form 4x - 6y = 18. We can rewrite this equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Solving for y in the given equation, we get y = (2/3)x - 3. So the slope of the given line is 2/3. Since the line we want to find is perpendicular, its slope will be the negative reciprocal of the given slope. Therefore, the slope of the new line will be -3/2. We also know that the new line passes through the point (1, 2). Using the point-slope form of the equation (y - y1 = m(x - x1)), where (x1, y1) is a point on the line and m is the slope of the line, we can write the equation of the new line as y - 2 = (-3/2)(x - 1). Simplifying this equation gives us the answer (B) y - 2 = -3/2(x - 1).