Let x = the length of the shorter piece
x+x+16=50in
2x=50-16
2x=34
x=17
Then
x+16=17+16
x+16=33
Subtract 16 from both sides
The lengths are 17in and 33in
Slope-intercept form is y = mx + b, and m is the slope
Because the slope is -3, m = -3
y = -3x + b
Plug in the point and solve for b
-7 = -3(-3) + b
-7 = 9 + b
-16 = b
a. y = -3x -16
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 .
Answer:
y+29103.83045673370361328125
