What is an equation of the line perpendicular to
y=1/5x+2 that contains (15,-4)

y + 4 = -5(x - 15)

Step-by-step explanation:

The given line has a slope of 1/5.  Any new line perpendicular to this given line has a slope which is the negative reciprocal of 1/5:  -5.

Use the point-slope equation of a line:  y - k = m(x - h), where (h, k) is the point through which the new line passes.  Here h = 15 and k = -4, so we have:

y + 4 = -5(x - 15)

This line is perpendicular to the given line and also passes through (15, -4).

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form