Question

Answer 20 points pls

Answer 1

The sum of slopes b and c is 0

This statement is NOT always true

Step-by-step explanation:

(1) According to the graph, line a and b are parallel to each other. This, therefore, means that they have the same slope/gradient.

(2) Line c however, is perpendicular to both lines a and b. The slope of two lines that are perpendicular to each other is always the negative inverse of the slope of the other. This means that the product of their slopes will become -1.

An example is that if the slope of a line is 2, then a line perpendicular to it will have a slop of – ½

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Answer 2

Answer:

The sum of the slopes of line b and line c is 0

Step-by-step explanation:

Verify each statement

case a) The sum of the slopes of line b and line c is 0

we know that

Line b and line c are perpendicular lines

If two lines are perpendicular, then their slopes are opposite reciprocal

If the slope of line c is n

then the slope of line b is -1/n

$-\frac{1}{n}+n=0$

Solve for n

$n^{2}=1$

$n=\pm1$

That means -----> This statement is true only when the slopes of the perpendicular lines are 1 and -1

therefore

NOT always true

case b) Line a and line b have the same slope

This statement is always true, because the lines are parallel

Remember that

If two lines are parallel, then the lines have the same slope

case c) The product of the slopes of line a and line c is -1

This statement is always true, because the lines are perpendicular

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

case d) The product of the slopes of line c and line b is -1

This statement is always true, because the lines are perpendicular

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)