Given equation of line y=0.25x-7.
On comparing given equation with slope-intercept form y=mx+b.
We get m=0.25.
0.25 could be written 25/100 in simplest fractions 1/4.
Line are perpendicular.
Therefore, slope of the perpendiular line would be reciprocal and opposite in sign of the given slope of the line.
Reciprocal of 1/4 is 4 and opposite of sign of 4 would be -4.
So, the slope of the required line is m=-4.
We are given a point (-6,8).
Applying point-slope form, we get
y-y1=m(x-x1)
y-8 = -4(x- (-6))
y-8 = -4(x+6)
y-8 = -4x -24.
Adding 8 on both sides, we get
y-8=8 = -4x -24+8
y=-4x-16.
Therefore, the equation y=-4x-16 is perpendicular to the given eqution of line.
Answer: (-2,5)
Step 1: Rewrite equations
-3x+2y=16
x-2y=-12
Step 2: Changing the second equation
With substitution, you have to already have the equation to solve for the specific variable (ex: x=y+1;y=x+1). Since the equation doesn’t give us one, we can flip the second equation to give us this.
Let’s add 2y on both sides.
x-2y=-12
+2y +2y
_________
x=2y-12
Now we have the equation to solve for x!
Step 3: Substituting
Now we need to substitute x into the first equation. Let’s do this now.
-3(2y-12)+2y=16
Step 4: Solving for y
-3(2y-12)+2y=16
*distribute*
-6y+36+2y=16
*combine like terms*
-4y+36=16
*subtract 36 on both sides*
-4y=-20
*divide both numbers by -4*
y=5
This is y! Now we need to solve for x.
Step 5: Solving for x
To find x, let’s just substitute y into the equation and solve
x=2y-12
x=2(5)-12
x=10-12
x=-2
Step 6: Ordered pair
(X,y) —> (-2,5)
This is your answer! Hope this helps comment below for more questions :)
Yes 2/3 is bigger because if u know there is the butterfly method try it search it up
(u^2 - 4) / (u-6)(u-2)
Resriction u ≠ 6 and u ≠ 2 (because the denominator cannot be equal lto zero)
Simplification
u^2 - 4 is a difference of two squares, then you can factor it as the product of (u+2)(u-2). So, you can write the expression as:
(u+2)(u-2) / (u-2)(u-6)
Simplify u -2 (because it appears in the numerator and the denominator)
(u + 2) / (u -6), with u ≠2 and u≠6
It does not matter which he does first. Either way, zero pairs will be created on both sides, which will isolate the variable to determine x<span>. Adding the </span>x<span>-tiles and then the unit tile, or visa versa, will give the same solution.</span>
