Question

What is the equation of a line that passes through the point (4, 11) and is perpendicular to the line whose equation is y= 4/3x + 7?

a) y = -3/4x + 14
b) y = -3/4x + 7
c) y = 3/4x + 11
d) y = 3/4x - 7

Answer 1

The equation of the line that passes through the point (4, 11) and is perpendicular to the given line is y = -3/4x + 14.

Step-by-step explanation:

To find the equation of a line that is perpendicular to the line y = (4/3)x + 7 and passes through the point (4, 11), we need to determine the slope of the new line. Since two lines are perpendicular if and only if the product of their slopes is -1, we can find the slope of the new line by taking the negative reciprocal of the slope of the given line.

The given line has a slope of 4/3, so the slope of the new line is -3/4. Using the point-slope form of a linear equation, we can write the equation of the new line as follows:

y - 11 = (-3/4)(x - 4)

Simplifying the equation gives us:

y = -3/4x + 14