Question

Write the equation of the line that is perpendicular to the line 2x+10y=20 through The given point (2,3). Do not use spaces in your equation

Answer 1

The first thing you want to do is figure out what the slope of line is.

the slope of a line in the format Ax+By=C is -A/B
so the slope of the line 2x+10y=20 is -2/10 which simplifies to -1/5

now that you know the slope of that line (i’ll call it line 1), you can use it to find the slope of the perpendicular line by taking the opposite reciprocal of the slope of line 1

slope of line 1: -1/5
opposite reciprocal of the slope of line 1 (which is the perpendicular line’s slope): 5

and since you now have a slope and a point, you can use point-slope [y-y₁=m(x-x₁)] form to write the equation of the line

m = 5
point (x₁y₁): (2,3)

point slope form:
y-(3)=(5)(x-(2))
y-3=5(x-2)

to slope intercept form
y=5x-10+3
y=5x-7

hope this helps :)