Question

What is an equation of the line that passes through the point ( − 4 , − 6 ) (−4,−6) and is perpendicular to the line 4 x + 5 y = 25 4x+5y=25?

Answer 1

Explanation:

Everyone asks about these types of problems, I feel like math teachers do not know how to teach this type of problem.

these really are just follow the steps , type of problems..

Step 1 :

find the slope

slope = m

given:

point P1 (-4,-6) in the form (x1,y1)

4x + 5y = 25

because they tell us to find a line perpendicular to the given line, we are able to use the slope of the given line to find the slope of the line we want. Perpendicular means take the reciprocal of the given line's slope.

or

4x + 5y = 25

5y = -4x + 25

y =
`(-4)/(5)` X +5 use the slope intercept formula to know slope m

y= mx + b

m=
`(-4)/(5)`

take the reciprocal and swap the sign

m =
`(5)/(4)`

Step 2:

put the given information into the point slope formula. if this seems like a lot to remember it's going to be super super helpful for you to memorize the two formulas, slope-intercept and point-slope, you'll use them over and over.

point slope formula

y - y1 = m(x -x1)

y - (-6) =
`(5)/(4)`(x-(-4))

the (x1,y1) came from the given point above. Now just solve for Y

y +6 =
`(5)/(4)`(x+4)

y + 6 =
`(5)/(4)`x + 5

y =
`(5)/(4)`x + 5 -6

y =
`(5)/(4)`x -1

this is the equation of the line that passes through point (-4,-6)

Note that that is in the form of the slope intercept formula

y = mx + b

where b is just a negative number

There was really just 2 Steps, and none of that math is really difficult.

recall the two formulas, and how they are used. and you are good.