Question

Which of the following options represents an equation for the line l1, which is perpendicular to f(x) = (1/3)x + 5 and passes through the point (1, -2)?

A) y = -3x + 1
B) y = -3x - 5
C) y = 3x + 1
D) y = 3x - 5

Answer 1

The equation for the line l1, perpendicular to f(x) = (1/3)x + 5 and passing through the point (1, -2), is A) y = -3x + 1.

Step-by-step explanation:

To find the equation of a line that is perpendicular to f(x) = (1/3)x + 5 and passes through the point (1, -2), we need to determine the slope of the given line. The given line has a slope of 1/3, so the line perpendicular to it will have a slope of the negative reciprocal, which is -3. Using the point-slope form of a linear equation, we can write the equation as:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point. Substituting the values, we have:

y - (-2) = -3(x - 1)

Simplifying the equation gives us:

y = -3x + 1

Therefore, the equation representing the line l1, which is perpendicular to f(x) = (1/3)x + 5 and passes through the point (1, -2), is y = -3x + 1.