Answer:
y=[tex]\frac{x}{2} - 2[/tex]
Step-by-step explanation:
y = [tex]\frac{x+12}{2}[/tex]
if it goes through 4,0 and has a gradient of x/2 the y-int is at -2.
therefore, y=[tex]\frac{x}{2} - 2[/tex]
Answer:
[tex]\large\boxed{y=\dfrac{1}{2}x-2\to -x+2y=-4}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
Let
[tex]k:y=m_1x+b_1,\ l:y=m_2x+b_2[/tex]
[tex]l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2[/tex]
Parallel lines have the same slope.
Convert given equation of a line to the slope-intercept form:
[tex]-x+2y=12[/tex] add x to both sides
[tex]2y=x+12[/tex] divide both sides by 2
[tex]y=\dfrac{1}{2}x+6[/tex]
The slope
[tex]m=\dfrac{1}{2}[/tex]
We have
[tex]y=\dfrac{1}{2}x+b[/tex]
Put the coordinates of the given point P(4, 0) to the equation:
[tex]0=\dfrac{1}{2}(4)+b[/tex]
[tex]0=2+b[/tex] subtract 2 from both sides
[tex]-2=b\to b=-2[/tex]
Finally we have:
[tex]y=\dfrac{1}{2}x-2[/tex]
Convert to the standard form (Ax + By = C):
[tex]y=\dfrac{1}{2}x-2[/tex] multiply both sides by 2
[tex]2y=x-4[/tex] subtract x from both sides
[tex]-x+2y=-4[/tex]
