Equation of a line that is perpendicular to given line is [tex]y=\frac{-7}{4} x+\frac{7}{4}[/tex].
Equation of a line that is parallel to given line is [tex]y=\frac{4}{7} x-\frac{69}{7}[/tex].
Solution:
Given line [tex]y=\frac{4}{7} x+4[/tex].
Slope of this line, [tex]m_1[/tex] = [tex]\frac{4}{7}[/tex]
[tex]$\text{Slope of perpendicular line} = \frac{-1}{\text{Slope of the given line} }[/tex]
[tex]$m_2=\frac{-1}{m_1}[/tex]
[tex]$=\frac{-1}{\frac{4}{7} }[/tex]
Slope of perpendicular line, [tex]m_2=\frac{-7}{4}[/tex]
Passes through the point (–7, 5). Here [tex]x_1=-7, y_1=5[/tex].
Point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]$y-(-7)=\frac{-7}{4} (x-5)[/tex]
[tex]$y+7=\frac{-7}{4} x+\frac{35}{4}[/tex]
Subtract 7 from both sides, we get
[tex]$y=\frac{-7}{4} x+\frac{7}{4}[/tex]
Equation of a line that is perpendicular to given line is [tex]y=\frac{-7}{4} x+\frac{7}{4}[/tex].
To find the parallel line:
Slopes of parallel lines are equal.
[tex]m_1=m_3[/tex]
[tex]$m_3=\frac{4}{7}[/tex]
Passes through the point (–7, 5). Here [tex]x_1=-7, y_1=5[/tex].
Point-slope formula:
[tex]$y-(-7)=\frac{4}{7} (x-5)[/tex]
[tex]$y+7=\frac{4}{7} x-\frac{20}{7}[/tex]
Subtract 7 from both sides,
[tex]$y=\frac{4}{7} x-\frac{69}{7}[/tex]
Equation of a line that is parallel to given line is [tex]y=\frac{4}{7} x-\frac{69}{7}[/tex].
