Question

Write an equation of the line passing through point P(4, 0)

Answer 1

Answer:

$\large\boxed{y=\dfrac{1}{2}x-2\to -x+2y=-4}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

Let

$k:y=m_1x+b_1,\ l:y=m_2x+b_2$

$l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2$

Parallel lines have the same slope.

Convert given equation of a line to the slope-intercept form:

$-x+2y=12$         add x to both sides

$2y=x+12$         divide both sides by 2

$y=\dfrac{1}{2}x+6$

The slope

$m=\dfrac{1}{2}$

We have

$y=\dfrac{1}{2}x+b$

Put the coordinates of the given point P(4, 0) to the equation:

$0=\dfrac{1}{2}(4)+b$

$0=2+b$              subtract 2 from both sides

$-2=b\to b=-2$

Finally we have:

$y=\dfrac{1}{2}x-2$

Convert to the standard form (Ax + By = C):

$y=\dfrac{1}{2}x-2$          multiply both sides by 2

$2y=x-4$         subtract x from both sides

$-x+2y=-4$

Answer 2

Answer:

y=$\frac{x}{2} - 2$

Step-by-step explanation:

y = $\frac{x+12}{2}$

if it goes through 4,0 and has a gradient of x/2 the y-int is at -2.

therefore, y=$\frac{x}{2} - 2$