Find the slope of a line perpendicular to the line whose equation is x, minus, 6, y, equals, 24x−6y=24. Fully simplify your answer.}

Answer 1

Hi Greydis,

First, a perpendicular line goes in the opposite direction on a coordinated point graph. So first is finding the slope of the equation, this can be found with the slope intercept form or y = mx + b where:

y = y-coordinate point on graph

m = slope of graph (rise over run)

x = x-coordinate point on graph

b = y-intercept point or point on y-axis where x = 0

So for example, an equation can be y = 2x + 1. The perpendicular line of this would be the negative inverse of m with the following equation: (-1) / m; OR y = (-1/2)x + 1

Now, looking at your above question of 24x - 6y = 24 we FIRST want to isolate the y value. We can do it through the following steps:

Given: 24x - 6y = 24

1. Subtract 24x from both sides
2. We would receive -6y = -24x + 24
3. Divide both sides by -6
4. We would receive y = 4x - 4

Next step is to define what our m is, so with the equation y = mx+b, we can substitute in the above equation we received. So our equation is y = 4x - 4 where:

y = y-coordinate point

m = 4

x = x-coordinate point

b = -4

So, in order to find a perpendicular line, we need to find the negative inverse of m in y = 4x - 4. We know that m in this equation is 4. Therefore the slope of our perpendicular line would be -1/4 since it would be (-1) / m which in this equation is 4. So plug and chug and you get (-1) / 4 or -1/4

Answer 2

 24x−6y=24

Let's rewrite the equation in the slope-intercept form: y = mx + b

-6y = -24x + 24

y = 4x - 4

slope m = 4

Perpendicular slope: m1 * m2 = -1

m1 = 4

4 * m2 = -1

m2 = -1/4

Hence, perpendicular slope is -1/4