Question

What is the equation of the line described below written in slope-intercept form?

the line passing through point (2, 2) and perpendicular to the line whose equation is y = x

y = x - 4
y = x + 4
y = -x + 4

Answer 1

y= -x + 4
since it is perpendicular the slope is turned the opposite direction and if you graph it out, it passes through the y-axis at (0,4) so the y-int is 4.

Answer 2

Answer:

The equation is $y=-x+4$

Step-by-step explanation:

We know that the line must pass through the point (2,2) so it must verify the equation ⇒

a) y = x - 4

b) y = x + 4

c) y = -x + 4

If we replace the point (2,2) in the equation a)

$y=x-4\\2=2-4\\2=-2$ that it is absurd. Therefore the point (2,2) does not belong to the line a)

If we replace the point (2,2) in the equation b)

$y=x+4\\2=2+4\\2=6$ therefore the point (2,2) does not belong to the line b)

Finally,

$y=-x+4\\2=-2+4\\2=2$ therefore the point (2,2) belongs to the line $y=-x+4$

given a line

$y=ax+b$

Where ''a'' is the slope. If we want to obtain a line which is perpendicular to this, we need to multiply by -1 the slope and reverse it ⇒

$y=ax+b$ is perpendicular to the line $y=(-\frac{1}{a})x+b$

Now, given the line y = x the slope is ''1'' ⇒ Any line with a slope of ''-1'' will be perpendicular

The slope of the line c) y = -x +4 is -1 ⇒ y = -x +4 is perpendicular to y = x

The correct answer is $y=-x+4$