Question

Please help :) I have no clue & math isn’t my strong subject.

Answer 1

Equation of a line that is perpendicular to given line is $y=\frac{-7}{4} x+\frac{7}{4}$.

Equation of a line that is parallel to given line is $y=\frac{4}{7} x-\frac{69}{7}$.

Solution:

Given line $y=\frac{4}{7} x+4$.

Slope of this line, $m_1$ = $\frac{4}{7}$

$\text{Slope of perpendicular line} = \frac{-1}{\text{Slope of the given line} }$

                                   $m_2=\frac{-1}{m_1}$

                                          $=\frac{-1}{\frac{4}{7} }$

Slope of perpendicular line, $m_2=\frac{-7}{4}$

Passes through the point (–7, 5). Here $x_1=-7, y_1=5$.

Point-slope formula:

$y-y_1=m(x-x_1)$

$y-(-7)=\frac{-7}{4} (x-5)$

$y+7=\frac{-7}{4} x+\frac{35}{4}$

Subtract 7 from both sides, we get

$y=\frac{-7}{4} x+\frac{7}{4}$

Equation of a line that is perpendicular to given line is $y=\frac{-7}{4} x+\frac{7}{4}$.

To find the parallel line:

Slopes of parallel lines are equal.

$m_1=m_3$

$m_3=\frac{4}{7}$

Passes through the point (–7, 5). Here $x_1=-7, y_1=5$.

Point-slope formula:

$y-(-7)=\frac{4}{7} (x-5)$

$y+7=\frac{4}{7} x-\frac{20}{7}$

Subtract 7 from both sides,

$y=\frac{4}{7} x-\frac{69}{7}$

Equation of a line that is parallel to given line is $y=\frac{4}{7} x-\frac{69}{7}$.