Question

What is the slope of a line perpendicular to the line whose equation is

5x – 2y = -10. Fully simplify your answer.

Answer 1

-2/5

Explanation:

5x - 2y = -10

-2y = -5x - 10

y = 5/2x + 5

m = 5/2

Perpendicular lines have slopes that are negative reciprocals of one another. For example, 5 would become -1/5 and 1/3 would become -3.

If m = 5/2

Perpendicular line m = -2/5

Hope this helps!

Answer 2

The slope of the line perpendicular to this line is -2/5.

Explanation:

5x - 2y = -10

Let's simplify this equation to be in slope-intercept form: y = mx + b.

Start by adding 2y to both sides of the equation.

• 5x = -10 + 2y

Next, add 10 to both sides of the equation.

• 5x + 10 = 2y

Divide both sides of the equation by 2.

• (5x + 10)/2 = y
• (5/2)x + 5 = y

The slope of this line is the coefficient of x; in this case, it is 5/2.

If we want to find the slope of the line perpendicular to this line, we take the opposite (change the sign) reciprocal (flip the fraction).

The slope 5/2 becomes -2/5.

Therefore, the slope of a line perpendicular to the line whose equation is 5x - 2y = -10 is -2/5.