ANSWER:
m = -3/4
b = -3
STEP-BY-STEP EXPLANATION:
We have that the equation in its slope-intercept form is the following:
We calculate the slope as follows:
To calculate the slope we use the intercepts that are (-4, 0) and (0, -3), we replace:
Now, the value of b would be -3, since the y-intercept is (0,-3), therefore, the equation would be:
Answer:
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To prove the QRST is a parallelogram.
Step 1: Given and
Step 2: are alternate interior angles.
Definition of alternate interior angles
Step 3: Alternate interior angle theorem:
If two parallel lines cut by a transversal then the alternate interior angles are congruence.
QR and TS are parallel lines cut by QS.
Therefore,
Step 4: Reflexive property of congruence:
Any geometric figure is congruence to itself.
Therefore,
Step 5: By the above steps
(Angle),
(Angle) and
(Side)
Hence (by ASA congruence theorem)
Step 6: Corresponding parts of congruence triangles are congruent.
Step 7: Property of parallelogram:
If one pair of opposite sides are both parallel and congruent, then the quadrilateral is a parallelogram.
Hence Quadrilateral QRST is a parallelogram.