Consider the line y = 5/2x.
what is the slope of a line perpendicular to this line?
what is the slope of a line parallel to this line?

Perpendicular: -2/5

Parallel: 5/2

Step-by-step explanation:

The slope-intercept formula is y=mx+b, where mx is the slope.

So in the equation y = 5/2x, 5/2 is understood as the slope.

To find a perpendicular slope you have to do the opposite (sign), reciprocal (flip denominator and numerator) of the original number.

Therefore 5/2 become negative, and then the numerator and denominator switch sides. (-2/5)

Parallel slope is the exact same as the original one so nothing changes. (5/2)

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