Answer:
see explanation
Step-by-step explanation:
13 (a)
Given
x + 2y = 3 ( subtract x from both sides )
2y = - x + 3 ( divide all terms by 2 )
y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{3}{2}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
(b)
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}{2} }[/tex] = 2
(c)
The partial equation of the perpendicular line is
y = 2x + b
To find b substitute (1, 4) into the partial equation
4 = 2 + b ⇒ b = 4 - 2 = 2
y = 2x + 2 ← equation of perpendicular line
