Answer:
The point slope formula is
(y−y1)=m(x−x1)
Where m = the slope calculated as y2−y1x2−x1
(x1,y1)(x2,y2)
(-4 , 1) (-2 , 3)
Solve for the slope
m = 3−1−2−(−3) = 21 = m = 2
(y−3)=2(x−(−2)) Plug in known values.
y−3=2(x+2) Simplify signs
y−3=2x+4 Use Distributive property
y=−2x+4+3 isolate the y variable
answer (y = −5x+7 ) Simplify
Step-by-step answer:
Please refer to attached image.
1. Quad PQRS is cyclic (all vertices on the same circle), so opposite angles are supplementary, meaning
that
angles QPS and QRS are supplementary =>
QPS+QRS=180 =>
QRS = 180 - 74 = 106
2. Triangle RSQ is isosceles with RS=RQ =>
angles RSQ and RQS are congruent.
3. Angle RSQ = (180 - 106) /2 = 74 / 2 = 37
4. QP is a diameter => angle QSP is a right-angle.
5. From (3) and (4) above,
angle RSP = 37+90 = 127
6. Since PQRS is cyclic, angles RQP and RSP are supplementary =>
RQP+RSP = 180 =>
x + 127 = 180 =>
x = 180 - 127 = 53 degrees.