Question

Which of the following equations represents a line that is perpendicular to
y = -4x+9 and passes through the point, (4, 5)?
A. y- x+5 B. y- *x+6
C. y = x+4 D. y --4x+4

Answer 1

For this case we have that if two lines are perpendicular, then the product of their slopes is -1.

If we have the following equation of the line:

$y = -4x + 9$

The slope is $m_ {1} = - 4$

Then yes:

$m_ {1} * m_ {2} = - 1\\m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {- 4}\\m_ {2} = \frac {1} {4}$

The equation of the new line will be:

$y = \frac {1} {4} x + b$

We substitute the point to find "b":

$5 = \frac {1} {4} (4) + b\\5 = 1 + b\\b = 5-1\\b = 4$

Finally, the equation is:

$y = \frac {1} {4} x + 4$

Answer:

$y = \frac {1} {4} x + 4$