Respuesta :
Answer:
Step-by-step explanation:
5x - 15y = 20 in slope-intercept form:
- Subtract 5x from both sides: -15y = -5x + 20.
- Divide both sides by -15: y = (5/15)x - 20/15.
- Simplify: y = (1/3)x - 4/3.
By comparing the equation to the slope-intercept form, we see that the slope is 1/3.
Determine the negative reciprocal of the slope:
- The negative reciprocal of 1/3 is -3/1, which simplifies to -3.
Therefore, the slope of a line perpendicular to the line 5x - 15y = 20 is -3.
Answer:
slope of perpendicular line = - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given the line with equation
5x - 15y = 20 ( subtract 5x from both sides )
- 15y = - 5x + 20 ( divide through by - 15 )
[tex]\frac{-15}{-15}[/tex] y = [tex]\frac{-5}{-15}[/tex] x + [tex]\frac{20}{-15}[/tex] , that is
y = [tex]\frac{1}{3}[/tex] x - [tex]\frac{4}{3}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{1}{3}[/tex]
given a line with slope m, then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3
