Please help me please hurry

KatRina [158]

$y = \frac{-1}{7}x -\frac{8}{7}$ is the equation of the line that is perpendicular to this line and passes through the point (6, -2)

y = 7x - 44 equation of the line that is parallel to this line and passes through the point (6, -2)

<em><u>Solution:</u></em>

<em><u>Given that line is:</u></em>

y = 7x - 9

<em><u>The equation of line in slope intercept form is given as:</u></em>

y = mx + b ------ eqn 1

Where, "m" is the slope of line and "b" is the y intercept

On comparing eqn 1 with y = 7x - 9 we get,

m = 7

<h3><u>Find the equation of the line that is perpendicular to this line and passes through the point (6, -2)</u></h3>

We know that,

Product of slope of a line and slope of line perpendicular to given is always -1

Therefore,

$7 \times \text{ slope of line perpendicular to it } = -1\\\\\text{ slope of line perpendicular to it } = \frac{-1}{7}$

Now find the equation of line:

$\text{ Substitute } m = \frac{-1}{7} \text{ and } (x, y) = (6, -2) \text{ in eqn 1}$

$-2 = \frac{-1}{7} \times 6 + b\\\\-2 = \frac{-6}{7} + b\\\\b = -2+\frac{6}{7}\\\\b = \frac{-14+6}{7}\\\\b = \frac{-8}{7}$

$\text{Substitute } m = \frac{-1}{7} \text{ and } b = \frac{-8}{7} \text{ in eqn 1}\\\\y = \frac{-1}{7}x -\frac{8}{7}$

Thus the equation of line perpendicular to given line is found

<h3><u>Find the equation of the line that is parallel to this line and passes through the point (6, -2)</u></h3>

Slopes of parallel lines are equal

Therefore, m = 7

<em><u>Substitute m = 7 and (x, y) = (6, -2) in eqn 1</u></em>

-2 = 7(6) + b

-2 = 42 + b

b = -44

<em><u>Substitute m = 7 and b = -44 in eqn 1</u></em>

y = 7x - 44

Thus equation of line parallel to given line is found

8 0

3 years ago

Juan has 150 baseball cards. He wants to distribute them evenly amongst himself and his 4 friends. How many cards does each pers

Amiraneli [1.4K]

Answer:

30

Step-by-step explanation:

Him plus his friend equals 5 and 150/3 is 30

So 150 divided by 5 is 30

4 0

3 years ago

How many cubic inches of water will the aquarium hold

Nostrana [21]

Answer:

about 1,620 cubic inches

Hope that was helpful.Thank you!

8 0

3 years ago

A triangle has angle measurements of 53°, 37°, and 90°. What kind of triangle is it?

DedPeter [7]

Right angle because it has a 90° angle

5 0

3 years ago

Which is a counterexample for the conditional statement shown? If three distinct points lie in a plane, then the points can form

lina2011 [118]

<h2>Answer:</h2>

We take the example of:

Three collinear points in a plane.

Then we may conclude that they will never form a triangle.

<h2>Step-by-step explanation:</h2>

We know that a conditional statement is given by:

If p then q

where p is the hypothesis of the statement and q is the conclusion of the statement.

Counter example for a conditional statement--

A counter example is an example that makes the general statement is false.

i.e. a example which fulfills the condition of the hypothesis but does not satisfy the conclusion of the given statement.

Here the statement is:

If three distinct points lie in a plane, then the points can form a triangle.

i.e. Hypothesis is: Three distinct point lie in a plane.

and conclusion is: The points form a triangle.

So we take a example as:

Three collinear points lie in a plane but they will never form a triangle.

3 0

3 years ago