Write an equation in point slope form for a line containing the point (2,3) and parallel to each of the following lines

Question

I'm trying to put x+y=1 in point slope form and then find the parallel to that using the point (2,3)

Answer 1

Hi Rivera;

Point-slope form is...

y-y₁=m(x-x₁)

You probably already know that m=slope.

I am assuming that x+y=1 is the line at issue.  It is in standard form.  Standard form is

Ax+By=C, A and B do not equal zero and A is greater than zero.

Let's convert x+y=1 into slope-intercept form of...

y=mx+b, m is slope and b is y-intercept, the value of y when x=0.

y=-x+1

The slope is -1.

The slope of the line parallel to this is also -1.

POINT-SLOPE FORMULA...

y-3=-1(x-2)

y-3=-x+2

Let's add 3 to both sides so that we may combine like terms of 2 and 3...

3+y-3=-x+2+3

y=-x+5

 

The slope perpendicular to -1 is 1.  It is the negative inverse.  The inverse of 1/1 is 1/1.  However, for example, if the slope is -2, the slope of the line perpendicular to this would be 1/2.