Answer:
3x + y = 20 and x - 2y = - 4
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 )
(a)
Given
3x + y = 17 ( subtract 3x from both sides )
y = - 3x + 17 ← in slope- intercept form
with slope m = - 3
Para;;el lines have equal slopes , then
y = - 3x + c ← is the partial equation
To find c substitute (4, 8) into the partial equation
8 = - 12 + c ⇒ c = 8 + 12 = 20
y = - 3x + 20 ← in slope- intercept form
Add 3x to both sides
3x + y = 20 ← in standard form
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(b)
Given
y + 2x = 13 ( subtract 2x from both sides )
y = - 2x + 13 ← in slope- intercept form
with slope m = - 2
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}{-2}[/tex] = [tex]\frac{1}{2}[/tex] , then
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (2, 3) into the partial equation
3 = 1 + c ⇒ c = 3 - 1 = 2
y = [tex]\frac{1}{2}[/tex] x + 2 ← in slope- intercept form
Multiply through by 2 to clear the fraction
2y = x + 4
x - 2y = - 4 ← in standard form
