Question

What is an equation of the line that passes through the point ( − 3 , − 1 ) and is perpendicular to the line x − 2 y =6

Answer 1

Answer: y = -2x - 7

Step-by-step explanation:

The equation for a perpenducular line has a slope that is the negative inverse of the reference line, in this case x - 2y = 6.

Let's put this equation into standard slope-intercept form, y = mx+b, where m is the slope and b the y-intercept (the value of y when x is 0).

x - 2y = 6

- 2y = 6 - x

y = (1/2) x -3

The slope is (1/2), so a perpendicular line will have a slope of -2.

y = -2x + b

We can find b by using the given point ((-3,-1), a known solution):

-1 = -2*(-3) + b

-1 = 6 + b

b = -7

The perpendicular equation is y = -2x - 7

y = -2x