Answer:
y = [tex]\frac{3}{2}[/tex] x - 11
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = - [tex]\frac{2}{3}[/tex] x + 5 is in this form
with m = - [tex]\frac{2}{3}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{3} }[/tex] = [tex]\frac{3}{2}[/tex], hence
y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
to find c substitute (8, 1) into the partial equation
1 = 12 + c ⇒ c = 1 - 12 = - 11
y = [tex]\frac{3}{2}[/tex] x - 11 ← equation of line
Answer:
[tex]y = \frac{3}{2} x-11[/tex]
Step-by-step explanation:
We have to find the equation a line which passes through the point (8, 1) and is perpendicular to a line with the equation [tex]y = - \frac{2}{3} x+5[/tex].
So the slope for this equation will be the negative reciprocal of the line which is perpendicular to it i.e. [tex]\frac{3}{2}[/tex].
Finding the y-intercept of the line:
[tex]y=mx+c[/tex]
[tex]1=\frac{3}{2} (8)+c[/tex]
[tex]c=-11[/tex]
Therefore, the equation of the line will be [tex]y = \frac{3}{2} x-11[/tex].
