When we factorise an expression, we are looking for simple factors that multiply to get the original expression. Usually it is very natural to factorise something like a quadratic in x. For example:
x^2 + 3x + 2 = (x+1)(x+2)
But there are other situations where factorisation can be applied. Take this quadratic:
x^2 - 9x = x(x-9)
This second example is closer to the question in hand. Just like x was a common factor to both x^2 and -9x, we are looking for a common factor to both 6b and 24bc. The common factor is 6b.
Hence 6b + 24bc = 6b(1 + 4c).
I hope this helps you :)
45/100 is 4,500%
2/5 is 40%
18/40 is 45%
15/25 is 60%
Step 1
<u>Find the slope of the given line</u>
we have
![3x+4y=15](https://tex.z-dn.net/?f=3x%2B4y%3D15)
Isolate the variable y
Subtract
both sides
![3x+4y-3x=15-3x](https://tex.z-dn.net/?f=3x%2B4y-3x%3D15-3x)
![4y=-3x+15](https://tex.z-dn.net/?f=4y%3D-3x%2B15)
Divide by
both sides
![y=-\frac{3}{4}x+ \frac{15}{4}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B3%7D%7B4%7Dx%2B%20%5Cfrac%7B15%7D%7B4%7D)
the slope of the given line is
![m=-\frac{3}{4}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B3%7D%7B4%7D)
Step 2
Find the equation of the line that passes through the point
and is parallel to the given line
we know that
if two lines are parallel, then their slopes are equal
The equation of the line into point-slope form is equal to
![y-y1=m(x-x1)](https://tex.z-dn.net/?f=y-y1%3Dm%28x-x1%29)
we have
![m=-\frac{3}{4}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B3%7D%7B4%7D)
substitute in the equation
![y+2=-\frac{3}{4}(x-8)](https://tex.z-dn.net/?f=y%2B2%3D-%5Cfrac%7B3%7D%7B4%7D%28x-8%29)
![y=-\frac{3}{4}x+6-2](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B3%7D%7B4%7Dx%2B6-2)
or ![3x+4y=16](https://tex.z-dn.net/?f=3x%2B4y%3D16)
therefore
<u>the answer is</u>
or
![3x+4y=16](https://tex.z-dn.net/?f=3x%2B4y%3D16)
Answer and workings in the attachment below.
We can verify this with the graph
(-6, 3) NO
(-3, 3) NO
(-5, 0) NO
(-4, 2) YES
(0,0) NO
(-6, 6) YES
(-3, -6) NO
(-4.0) YES
the area where the solutions are in the yellow area