Question

What is the slope of the line perpendicular to the line through the points (-1,6) and (3,-4)

Answer 1

The slope of the line perpendicular to the line through the points (-1,6) and (3,-4) is -5/2.

Step-by-step explanation:

We have to find the slope of the line perpendicular to the line through the points (-1,6) and (3,-4).

using the formula;-

m = (y²-y¹) / (x²-x¹)

Where,

• m = slope
• ( y² - y¹) = ( -4 -6 )
• ( x² - x¹) = ( 3 - 1)

plug the value and simplify.

m = ( (-4 ) - 6)/(3 - (- 1)

m = - 10 / 4

m = - 5/2

Hence, The slope of the line perpendicular to the line through the points (-1,6) and (3,-4) is -5/2.

Answer 2

The slope of the perpendicular line is 2/5.

Explanation:

We want to find the slope of the line that is perpendicular to the line that passes through the points (-1, 6) and (3, -4).

Recall that the slopes of perpendicular lines are negative reciprocals of each other.

Find the slope of the original line:

`\displaystyle m=(\Delta y)/(\Delta x)=((-4)-(6))/((3)-(-1))=(-10)/(4)=-(5)/(2)`

The slope of the perpendicular line will be its negative reciprocal.

Thus, the slope of the perpendicular line is 2/5.