Question

Help me I keep getting it wrong

Answer 1

Answer:

see explanation

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 = $\frac{2}{3}$ x - 6 ← is in slope- intercept form

with slope m = $\frac{2}{3}$

Parallel lines have equal slopes , then

y = $\frac{2}{3}$ x + c ← is the partial equation

To find c substitute (9, 2) into the partial equation

2 = 6 + c ⇒ c = 2 - 6 = - 4

y = $\frac{2}{3}$ x - 4 ← equation of parallel line

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Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{2}{3} }$ = - $\frac{3}{2}$ , then

y = - $\frac{3}{2}$ x + c ← is the partial equation

To find c substitute (9, 2) into the partial equation

2 = - $\frac{27}{2}$ + c ⇒ c = 2 + $\frac{27}{2}$ = $\frac{31}{2}$

y = - $\frac{3}{2}$ x + $\frac{31}{2}$ ← equation of perpendicular line