Write an equation of the line that passes through (−4,−1) and is perpendicular to the line y=43x+6.

The equation in the problem in written in slope-intercept form (i.e.  y= mx + b) where the slope (m)  is 4/3 and the y-intercept (b)  is 6.

When lines are perpendicular, their slopes are negative reciprocals.  So the slope of the line perpendicular to the one in the problem is -3/4.  

The new equation for the perpendicular line will be:  y = -3/4x + b

We can use the given point to determine the y-intercept for the perpendicular line by substituting x as -4 and y as -1 and solving for the y-intercept b.

y = -3/4 x + b

-1 = (-3/4)*(-4) + b

-1= 3 + b

-1 -3 = 3 + b - 3

-4 = b

So the equation of the perpendicular line is:  y = -3/4 x - 4

Step-by-step explanation:

y = -3/4 x - 4

Step-by-step explanation:

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