Let’s start by considering any 2 points falling on the line, the intercepts are the ones which come to my mind. Thus, the line 2x+3 will originally intersect the x- axis at (−32,0) and the y- axis at (0,3).
So, the basic insight is that on rotating the origin, the axes rotate. But the intercepts (their lengths) don’t change. The axis that is being intercepted will change, not the distance of intercepting points from the origin until our line is itself rotated. (Keep scribbling)
For the first case, we rotate the axes clockwise by a right angle. Now notice that the negative x-axis replaces the positive y-axis. So, our line now intercepts the negative x- axis at a distance 3 from the origin. Similarly, the negative y- axis replaces the negative x- axis. So, our line intersects the negative y- axis at distance 1.5 .
Therefore, the new intercepts are X(−3,0) and Y(0,−1.5). We can hence produce the new equation for our line in the slope- intercept form as
y=−x2−1.5 .
Similarly, you can imagine the other cases as axes rotation/replacement.
For 180∘, the equation would be y=2x−3 .
For 270∘, the equation would be y=−x2+1.5 .
What is the question asking?
Answer:
Ladonna: a + c + b
Step-by-step explanation:
-The commutative property in addition states that the order of arrangement of the integers to be added has no effect on their sum such that:
-Since the alphabet follows the order a,b, c....
Only Ladonna rearranged to change this order to show the commutative property.
-Hence, Ladonna wrote the expression correctly.
*The commutative property should not be confused with the associative property.
-The latter allows you to change the order and terms within the closed parentheses while retaining the answer.
About 6.5 I believe, I looked it up and a gross was a total of 144 of something, also known as a dozen dozen.
5x-y+3=0
-y = -5x-3
y = 5x+3
Y = mx+b
M = slope = 5/1 = 5
B = y intercept = 3 = (0,3).
