The perpendicular line would have a slope of 1/3.
Perpendicular lines have opposite and reciprocal slopes. So first we have to find the slope of the original line. We can do this by solving the equation for y.
5x - 9y = 1
-9y = -5x + 1
y = 5/9x - 1/9
To do the opposite, take the original slope (5/9) and change the sign (-5/9).
To do the reciprocal, take the slope we changed (-5/9) and flip it as a fraction (-9/5).
This gives us a new slope of
Trying to factor by splitting the middle term
Factoring <span> b2-4b+4</span>
The first term is, <span> <span>b2</span> </span> its coefficient is <span> 1 </span>.
The middle term is, <span> -4b </span> its coefficient is <span> -4 </span>.
The last term, "the constant", is <span> +4 </span>
Step-1 : Multiply the coefficient of the first term by the constant <span> 1 • 4 = 4</span>
Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is <span> -4 </span>.
<span><span> </span></span>
<span><span>-4 + -1 = -5</span><span> -2 + -2 = -4 That's it</span></span>
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and -2
<span>b2 - 2b</span> - 2b - 4
Step-4 : Add up the first 2 terms, pulling out like factors :
b • (b-2)
Add up the last 2 terms, pulling out common factors :
2 • (b-2)
Step-5 : Add up the four terms of step 4 :
(b-2) • (b-2)
Which is the desired factorization
To factor first multily 100 and 1 and get 100
then find what 2 numbers multiply to get 100 and add to get 20
the numbers are 10 and 10
so
split the center term up
100x^2+10x+10x+1
group
(100x^2+10x)+(10x+1)
undistribute
(10x)(10x+1)+(1)(10x+1)
undistribute/reverse distributive property
(10x+1)(10x+1)
(10x+1)^2
