Question 1 (essay worth 10 points) (01.01 mc) part a: parallel lines are two lines that never meet. find an example that contradicts this definition. how would you change the definition to make it more accurate

Answers

The parallel lines will never intersect.

According to the statement

we have to prove that the parallel lines are two lines that never meet.

So, for this purpose, we know that the

Two lines are said to be parallel when their slopes are equal.

Every line can be written in a generalized form as

y= mx+c

Where x, y are two coordinates in axis system.

C is intercept of line on y axis ( coordinate where the line intersects X axis)

M is slope of line, it indirectly tells us inclination (Theta ‘θ’ : it is the angle that the line makes from positive x axis) .

value of m can be determined as

m=tan θ

Thus if lines are parallel both line equations will have same slope that is same angle (inclination) with x axis.

If you want to find if these lines intersect, the intersection point will satisfy both equations of line.

If you try to solve both equations of line for value of x and y using method of simultaneous equations, you will notice that there is no solution to these equations.

This means that these two lines don’t have any point in common.

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