Find an equation of the line L that passes through the point

Question

(−2, 6)
and satisfies the given condition. (Let x be the independent variable and y be the dependent variable.)
L is perpendicular to the line
4x + 5y = 10

Answer 1

given line: 4x + 5y = 10 ----> slope = -4/5

so the slope of your new line is 5/4
and its equation must be
5x - 4y = C

plug in (−2, 6), find C
and you are done

Answer 2

perpendicular to 4x + 5 y = 10
well what slope
5 y = -4 x + 10
m = -4/5
so we want slope perpendicular to that
m' = -1/m = 5/4
so our line is
y = (5/4) x + b
so what is b ?
put the point in
6 = (5/4)(-2) + b
6 * 4 = -10 + 4 b
4 b = 24+ 10 = 34
b = 34/2
so our linne is
y = (5/4) x + 34/2
or
4 y = 5 x + 68
4 y - 5 x = 68
check my arithmetic, going fast

Answer 3

is the answer 5x-4y=-34 ?

Answer 4

yes, I have an arithmetic error

Answer 5

4 b = 24+ 10 = 34
b = 34/4
so our linne is
y = (5/4) x + 34/4
or
4 y = 5 x + 34
4 y - 5 x = 34
or
5 x - 4 y = -34