Find the equation of a line with the properties given. Write the equation in the form indicated.
-Through (4, 4) and perpendicular to the line whose equation is function notation
A) y = 7x - 32
C) f(x) = -7x + 32
D) f(x) = -7x - 32

Question

Find the equation of a line with the properties given. Write the equation in the form indicated.
-Through (4, 4) and perpendicular to the line whose equation is  function notation
A) y = 7x - 32 
C) f(x) = -7x + 32 
D) f(x) = -7x - 32

Quizplus · Accepted Answer

The given line has the equation y = 7x - 32. To find a line perpendicular to this line, we need to find its slope and take the negative reciprocal. The slope of the given line is 7. The negative reciprocal of 7 is -1/7, so the slope of the perpendicular line is -1/7.

We also know that the new line passes through the point (4,4). We can use the point-slope form of a line to find the equation:

y - y1 = m(x - x1)

where m is the slope and (x1,y1) is the given point.

Plugging in the values, we get:

y - 4 = (-1/7)(x - 4)

Simplifying and rearranging, we get:

y = -1/7 x + 4 + 4/7

or

y = -1/7 x + 32/7

This can also be written as

f(x) = -1/7 x + 32/7

Find the Equation of a Line with the Properties Given