Question

A line passes through the point (2,-5) and is perpendicular to the line with the equation y = -1/5x+5. What's the equation of the line?
A. y=-5x+5
B. y=1/5x+1
C. y=1/5x+5
D. y=5x-2

Answer 1

The equation of the perpendicular line is y = 5x - 15 ⇒ not in the choices

Step-by-step explanation:

Perpendicular lines have:

• Slopes their product is -1
• If the slope of one of them is $\frac{a}{b}$ , then the slope of the other is $\frac{-b}{a}$
• To find the slope of a perpendicular line to a given line reciprocal the slope of the given line and opposite its sign

The slope-intercept form of a linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept

∵ The equation of the given line is y = $-\frac{1}{5}$ x + 5

- Compare it with the form of the equation above

∴ m =  $-\frac{1}{5}$

∴ The slope of the given line is  $-\frac{1}{5}$

- Reciprocal it and opposite the sign to find the slope of the

   perpendicular line to it

∴ The slope of the perpendicular line = 5

- Substitute m in the form of the equation by 5

∵ y = 5 x + b

- To find by substitute x and y in the equation by the coordinates

   of any point on the line

∵ The perpendicular line passes through point (2 , -5)

∴ x = 2 and y = -5

∵ -5 = 5(2) + b

∴ -5 = 10 + b

- Subtract 10 from both sides

∴ -15 = b

∴ y = 5 x - 15

The equation of the perpendicular line is y = 5x - 15

Learn more:

You can learn more about the slope of a line in brainly.com/question/1979240

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