MATH SOLVE

5 months ago

Q:
# What is the equation of the line that is perpendicular to the given line and passes through the point (5, 3)

Accepted Solution

A:

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:[tex]y = mx + b[/tex]Where:m: It's the slopeb: It is the cut-off point with the y axisAccording to the figure, the line goes through the following points:[tex](x_ {1}, y_ {1}) :( 8, -10)\\(x_ {2}, y_ {2}): (- 8,10)[/tex]We found the slope:[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {10 - (- 10)} {- 8-8} = \frac {10 + 10 } {- 16} = \frac {20} {- 16} = - \frac {5} {4}[/tex]By definition, if two lines are perpendicular then the product of their slopes is -1:[tex]m * - \frac {5} {4} = - 1\\m = \frac {-1} {- \frac {5} {4}}\\m = \frac {4} {5}[/tex]Thus, the equation is of the form:[tex]y = \frac {4} {5} x + b[/tex]If the line goes through [tex](x, y) :( 5,3)[/tex]we have:[tex]3 = \frac {4} {5} (5) + b\\3 = 4 + b\\3-4 = b\\-1 = b[/tex]Finally, the equation is:[tex]y = \frac {4} {5} x-1[/tex]Algebraically manipulating we have:[tex]y + 1 = \frac {4} {5} x\\5y + 5 = 4x\\4x-5y = 5[/tex]Answer:Option A