What is the y-intercept of the line perpendicular to the line y = 4/3x + 1 that includes the point (4, 1)? A)2
B) -13/3
C) 4
D) -19/3

C) 4

Step-by-step explanation:

Hi there!

We are given the line y=4/3x+1

We want to find the y intercept of the line perpendicular to that line, that also passes through the point (4,1)

Perpendicular lines have slopes that have a product of -1

We'll first find the slope of y=4/3x+1

The equation is written in slope-intercept form (y=mx+b), where m is the slope and b is the y intercept

4/3 is in the place of where m (the slope) is, so the slope of the line is 4/3

Now to find the slope perpendicular to it, use this formula:

4/3m=-1

Multiply both sides by 3/4

m=-3/4

The slope of the line perpendicular to y=4/3x+1 is -3/4

We can write the equation of the new line in slope-intercept form as well; start by substituting -3/4 as m:

y=mx+b

y=-3/4x+b

Now we need to find b (y intercept)

As the equation includes the point (4,1), we can use it to help solve for b

Substitute 4 as x and 1 as y:

1=-3/4(4)+b

Multiply

1=-3+b

Add -3 to both sides

4=b

The y intercept of the line is 4

Hence, the answer is C

Hope this helps!

4

Step-by-step explanation:

If i did it right you would use the formula y-y1=m(x-x1)

Plug in y-1=-3/4(x-4)

-3/4 because perpendicular you need to flip and make negitive.

Distribute  y-1=-3/4x-12/4

move the one over y=-3/4x+4

4 being the y-intercept and -3/4 being the slope

Hope this helps!

yes

step-by-step explanation:

c

step-by-step explanation:

there is vertical asymptote at x = 2 and x = 0

vertical asymptote occurs at the points where the denominator is 0. so we can say that

x = 2 occurs when there is a factor (x-2) in the denominator, and

x = 0 occurs when there is a factor "x" in the denominator

thus, the denominator of the equation would have "x * (x-2)", this is option c only. that's the correct answer.