Question

Which equation is perpendicular to 5x-10y=6 and passes through (2,1)

Answer 1

y= -2x+5

Explanation:

Y=mx+b m = slope b = y-intercept

First for the equation 5x-10y=6. Solve for Y

• Move the 5x to the other side. -10y = 6 - 5x

• Divide -10 by both sides.
  `(-10y)/(-10)` =
  `(6)/(-10)` -
  `(5x)/(-10)`
• Simplify
  `(-10y)/(-10)` to y
• Simplify
  `(6)/(-10)` to -
  `(3)/(5)`
• Simplify
  `(5x)/(-10)` to
  `(x)/(-2)` (this can also be written as) -(1/2)x

• Now your equation is y = -(3/5) - -(1/2)x

• We know that 2 negatives makes a positive so it changes to

y= -(3/5) + (1/2)x

• Because of order of operations and we want to end up with an equation that matches y=mx+b form, switch the -(3/5) and +(1/2)x

• Now we have our end equation y=(1/2)x - (3/5)

Now we need to make a different equation following y=mx+b format that is perpendicular to y=(1/2)x - (3/5) and passes through (X,Y) or (2,1)

(when I do this I like to use the desmos graphing calculator online to make sure I'm correct)

Start with the slope...

To make a slope perpendicular you need to switch it from pos to neg or neg to pos. In this situation we switch from positive to negative. Then flip the fraction.

• Our slope is 1/2 so make it neg --> -(1/2)
• then flip the fraction --> -(2/1)
• our final slope is -2

So we can put this in our new equation. y = -2x + b

Now we need to find b...

Since they gave us the points (2,1) we can substitute those numbers into our new equation to find the value of b

• In the points (2,1) we know that x=2 and y=1
• Now we want to put the x and y values into y = -2x + b
• 1 = -2(2) + b
• Simplify -2(2) = -4 Now we have 1=-4 + b
• Move the -4 to the other side 5=b
• Now take out the x and y substitutes and add your 5 in for b in your new equation

• Final answer should be y= -2x+5