To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.
1. The first equation is - 2x + 5y = 0
Second equation is 
5y = 2x
- 2x + 5y = 0
Hence, the two equations are equivalent.
2. 




Hence, the equations are consistent.
3. 




Hence, the equations are consistent.
4. Equations can be re-arranged as:
x + y - 4 = 0 and
x + y + 6 = 0







Hence, the equations are inconsistent.
5. If we multiply the first equation by 4, we will get,
2y = -4x + 20 which is the second equation.
Hence, the equations are equivalent.
Answer:
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Step-by-step explanation:
<u>Finding the unit rate of the graph</u> :
- Take 2 points and find the slope
- ⇒ (0,0) and (12, 25)
- ⇒ m = 25 - 0 / 12 - 0
- ⇒ m = <u>25/12</u>
- The equation is : <u>y = 25/12x</u>
Now, the equations with greater unit rates (in increasing order) are :
Answer:
Δ MNQ ≅ Δ POQ ( BY Angle Angle Side)
Step-by-step explanation:
Given:
m∠NQM = 40°
m∠NQO = 100°
MNOP is a Rectangle
So we can say that:
Property of rectangle:
All angles of rectangle are 90°
Opposite sides of Rectangle are equal and parallel to each other
MN ≅ PO (opposite side of rectangle)
∠NMQ ≅ ∠OPQ (Both angles are 90°)
Now By Straight Angle property
m∠NQM + m∠NQO + m∠OQP = 180° (angles of straight line)
Substituting the values we get;
40° + 100° + m∠OQP = 180°
140° + m∠OQP = 180°
m∠OQP = 180° - 140° = 40°
So m∠OQP = m∠NQM = 40°
m∠OQP ≅ m∠NQM (Equals angles are congruent to each other)
Hence In Δ MNQ and Δ POQ
m∠OQP ≅ m∠NQM
∠NMQ ≅ ∠OPQ (Both angles are 90°)
MN ≅ PO (opposite side of rectangle)
Δ MNQ ≅ Δ POQ ( BY Angle Angle Side)
Hence Proved...