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Sunny_sXe [5.5K]
3 years ago
5

1) Write the equation parallel to the following equations that would go through (2,7):

Mathematics
1 answer:
myrzilka [38]3 years ago
5 0

<u>Note: </u><u><em>Your option 'b' is somewhat ambiguous, so I am assuming you meant to write the equation y=2x+3 for the 'b' option.</em></u>

Answer:

the equation y = 2x + 3  has slope m=2 and the y-intercept is 3, and also PASSES through the point (2, 7).

Step-by-step explanation:

  • An equation parallel to the given line equation will have the same slope.

Given the point (2, 7) from which the equation passes through.

so checking all the equations in the options to check whether any equation passes through or not.

Checking the option 'a':

y = 3x - 2

Putting (2, 7)

7=3(2)-2

7=6-2

7=4

L.H.S is not equal to R.H.S

Therefore, the option 'a' is NOT correct.

So, the equation y = 3x - 2 will NOT PASS through the point (2, 7)

Checking the option 'b':

y = 2x + 3

Putting (2, 7)

7=2(2)+2

7=7

7=7

L.H.S is equal to R.H.S

Therefore, option 'b' is the CORRECT option.

So, the equation y = 2x + 3 will PASS through the point (2, 7)

Checking the option 'c':

y = x-6

Putting (2, 7)

7=2-6

7=-4

L.H.S is not equal to R.H.S

Therefore, the option 'c' is NOT correct.

So, the equation y = x-6 will NOT PASS through the point (2, 7)

Checking the option 'd':

y + 2x = 8

Putting (2, 7)

7+2(2)=8

7+4=8

11=8

L.H.S is not equal to R.H.S

Therefore, the option 'd' is NOT correct.

So, the equation y + 2x = 8 will NOT PASS through the point (2, 7)

Therefore, considering the above analysis, we conclude that:

Option 'b' is the CORRECT option.

So, the equation y = 2x + 3 will PASS through the point (2, 7).

also

The slope-intercept form of the equation is

y=mx+b

where m is the slope and b is the y-intercept.

Therefore, the equation y = 2x + 3  has slope m=2 and the y-intercept is 3, and also PASSES through the point (2, 7).

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The similarities are;

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The differences are;

  • Two points of intersection of arcs are used in the segment bisector while only one is requited in an angle bisector
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The sources of the above equations are as follows;

The steps to construct a segment bisector are;

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  • Widen the compass so as to extend more than half of the length of the segment to be bisected
  • Draw two arcs, one above, and the other below the line
  • Place the compass needle at the other end and with the same compass width draw arcs that intersects with the arcs drawn in the above step
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The steps to construct an angle bisector are;

  • With the compass needle at the vertex, open the pencil end such that arcs can be drawn on the rays (lines) forming the angle
  • Draw an arc on both lines forming the angle
  • Place the compass needle at one of the intersection points and draw an arc in between the lines forming the angle
  • Repeat the above step with the same compass width from the other intersection point with the rays forming the angle
  • Join the point of intersection of the two arcs to the vertex of the angle to bisect the angle

Therefore, we have;

The similarities are;

  • A compass and a straight edge can be used for both construction
  • A straight line is drawn from the point of intersection of arcs to bisect the segment or the angle
  • The arcs are drawn from the ends of the segment or angle to be bisected
  • The width of the compass is more than half the width of the line or angle when drawing the arcs

The differences are;

  • In a segment bisector, the intersection point is above and below the line, while in an angle bisector only one pair of arcs are drawn to intersect above the line
  • The bisecting line passes through the segment being bisected, while the line stops at the vertex in an angle bisector

Learn more about the construction of segment and angle bisectors here;

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Step-by-step explanation:

From the provided statement.

The statement is: If Smith is guilty, then Jones is innocent.

The converse is: If Jones is innocent, then Smith is guilty.

The combination of a conditional statement and its converse is called biconditional statement.

The biconditional statement contains if and only if phrase between two part of the statement.

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Therefore, the required biconditional statement is: If Smith is guilty, if and only if Jones is innocent.

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