Through points (3,1) and perpendicular to x = 0, write the equation in slope-intercept form.

Question

I would like help on how to find an equation perpendicular in this sort of situation, it would help me a lot thank you.

Answer 1

Hi Riley W.,

We can use y = mx + b to show the line at x = 0 is y = b:

y = m*0 + b

y = b

From this we might see that the line x = 0 in a line on the y-axis.

We can also use the slope m = y/x for the line x = 0:

m = y/0

m = ∞

From this we see Infinite slope that is a vertical line. A vertical line at x = 0 is a line on the y-axis.

For a perpendicular line to an infinite slope we can take the negative reciprocal m = -x/y:

m = -0/y

m = 0

For the point given (3, 1) we can use y - y₁ = m*( x - x₁) with m = 0:

y - 1 = 0*( x - 3)

y = 1 (the answer)

I hope this helps, Joe.

Answer 2

the line x=0 is the y-axis

a line perpendicular to the y-axis must be parallel to the x-axis

also, this line must go through the point (3,1)

go right 3 units and up 1 unit and draw a line parallel to the x-axis going through this point and perpendicular to the y-axis

on this line y is always equal to 1 no matter what the x value is

the equation of this line is y=1

to help you, any line of the form x=a is a vertical line and any line of the form y=b is a horizontal line

Answer 3

Hi Riley,

If you use the point-slope form of a line, you need the slope and one point. To find the slope of a line perpendicular to x=0, you will need to realize that you have a vertical line. Any slope perpendicular to that is a horizontal line. Every horizontal line has a slope of zero.

Therefore, using the point-slope form is y-1=0(x-3). Your answer is y=1.

Dr. V

Answer 4

Always make a plot (graph) for this kind of thing. x = 0 is a vertical line, A perpendicular line will simply have a y value. You are given the point (3,1), so your new line will simply be y = 1.