Mathematics, 04.07.2019 17:00 erika6072

How can you find the equation of a line that is parallel/perpendicular to a given line

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Answer from: PaMuth1100

In the Slope-Intercept Form, m is the slope and b is the y-intercept.

Finding The Equation of a Line Parallel to the Given Line: Let the given line be line a and the parallel line be line b.

1) Find the slope of line a.

Example: Line a --> y = 5x + 2 . The slope is 5.

2) Find the y-intercept of line b.

To do this, you need to be given the coordinates of a point located on line b.

Example: The slope is 5 and the point is (2, 3), use the Slope-Intercept Formula, y=mx+b ---> 3 = 5(2) + b . Then you solve for b.

3 = 5(2) + b

3 = 10 + b

3 - 10 = 10 - 10 + b

-7 = b b=-7

The y-intercept of line b is -7

3) Finally, plugin the slope and the y-intercept into the Slope-Intercept Form.

Example: The slope of line b is 5 and the y-intercept is -7. The equation of line b is y = 5x - 7 .

Finding The Equation of a Line Perpendicular to The Given Line: Let the given line be line a and the perpendicular line be line b.

1) Find the opposite reciprocal of the slope of line a.

Example: Line a --> y=5x+2 . The slope is 5, to find the opposite reciprocal of the slope you use n --> $-\frac{1}{n}$ . In this case, it would be $-\frac{1}{5}$ . The opposite reciprocal of the slope of line a is $-\frac{1}{5}$ , which would be the slope of line b.

2) Find the y-intercept of line b.

To do this, you need to be given the coordinates of the point where line a and line b both intersect.

Example: The slope of line b is $-\frac{1}{5}$ and the point is (1, 7), use the Slope-Intercept Formula, y=mx+b ---> $7=-\frac{1}{5}(1) + b$ . Then you solve for b.

$7=-\frac{1}{5}(1) + b$

$7=-\frac{1}{5} + b$

$7+\frac{1}{5}=-\frac{1}{5} + \frac{1}{5} + b$

$7\frac{1}{5} =b$ $b=7\frac{1}{5}$

The y-intercept of line b is $7\frac{1}{5}$ .

3) Finally, plugin the slope and the y-intercept into the Slope-Intercept Form.

Example: The slope of line b is $-\frac{1}{5}$ and the y-intercept is $7\frac{1}{5}$ . The equation of line b is $y=-\frac{1}{5}x+7\frac{1}{5}$ .

Answer from: Quest

there are no figures how am i supposed to answer this question

step-by-step explanation:

Answer from: Quest

false

step-by-step explanation:

false. two legs of the trapezoid would be congruent, but the other two would not. were all the legs congruent, then we'd have a square; were the 2 shorter sides congruent and the 2 longer sides also congruent, we'd have a rectangle.

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