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 )
(10)
given
y = [tex]\frac{3}{2}[/tex] x + 4 ← in slope- intercept form
with slope m = [tex]\frac{3}{2}[/tex]
• Parallel lines have equal slopes , then
y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
to find c, substitute (- 4, 0 ) for x and y in the partial equation
0 = [tex]\frac{3}{2}[/tex] (- 4) + c = - 6 + c ( add 6 to both sides )
6 = c
y = [tex]\frac{3}{2}[/tex] x + 6 ← equation of parallel line
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(11)
given
y = - [tex]\frac{1}{3}[/tex] x + 5 ← in slope- intercept form
with slope m = - [tex]\frac{1}{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{1}{3} }[/tex] = 3 , then
y = 3x + c ← is the partial equation
to find c, substitute (12, 0 ) for x and y in the partial equation
0 = 3(12) + c = 36 + c (subtract 36 from both sides )
- 36 = c
y = 3x - 36 ← equation of perpendicular line
