Find the equation of a line perpendicular to y=X+6 that passes through the point (3,1)

Answer 1

What is the slope, m, of the line y = x + 6?

What is the negative reciprodal, -1/m, of that value?

Use -1/m for the slope in point-slope form

(y - 1) / (x - 3) = -1 / m

All of this covered in Algebra 1.

Answer 2

There are (basically) two ways to fully define a line:

1. Know the slope and one point that are on the line.
2. Know two points that are on the line (which would let you figure out the slope anyway).

Here we use option 1, since the question happens to give us one point and information about the slope (being perpendicular to another line).

Find the slope.

We know that the line is "perpendicular to y=X+6".

y = x + 6 is in the form of y = mx + b, which means m (aka the slope) = 1.

A perpendicular line would have a slope of -1/m, aka the reciprocal times negative 1.

Find one point.

This one's easy - you are given a point.

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Now that you have the slope and a point, you can write the equation of your new line in point slope form, aka:

y - y1 = m * (x - x1)

Where x1 and y1 are the coordinates of the aforementioned point on the line, and m is the slope (of the new line, not the old one we were comparing it to!). (And "y" and "x" are literally the variables y and x)