Y = 3x + 1
Parallel lines have the same slope so the slope would be 3. Take the given equation and add the 3x to the other side. Using the given point. -2 (y point) = 3(-1(x point)) + b. Solve for b by adding the 3 over. b = 1 which is your y intercept.
Answer:
In parallelogram ABCD
FD is perpendicular to BC
BE is perpendicular to CD
Consider triangle BEC and triangle DFC
FC = EC (Given)
Angle BEC = Angle DFC (=90°)
Angle BCE = Angle DCF (common)
Therefore triangle BEC is congruent to triangle DFC (AAS congruency)
DF = BE (CPCT)
Since the altitudes are equal their bases will also be equal
Therefore BC = DC
Therefore BC = DC = AD = AB
Therefore ABCD is a rhombus
Hope this helps!
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Answer:
We conclude the equation is linear because it can be rewritten in the form
.
Hence, option D is correct.
Step-by-step explanation:
The slope-intercept form of the line or linear equation
where
is the slope
is the y-intercept
<u>Important Tip:</u>
The graph of a linear equation is always a straight line.
Convert the given equation in the slope-intercept form

subtract 18x from both sides

simplify

divide both sides by 9

Now, comparing the equation
with a slop-intercept form of linear equation
- The y-intercept b = -416/9
Therefore, we conclude the equation is linear because it can be rewritten in the form
.
From the attached graph, is also clear that the graph of the equation
is a straight line.
Hence, option D is correct.
Answer:
I believe it is A because if you use the slope x it matches with the line.
The inclusion/exclusion principle states that

That is, the union has as many members as the sum of the number of members of the individual sets, minus the number of elements contained in both sets (to avoid double-counting).
Therefore,

will have the most elements when the sets

and

are disjoint, i.e.

, which would mean the most we can can in this case would be

(Note that

denotes the cardinality of the set

.)