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A straight line can be written in the form y=mx+b, where m is the slope and b is the y-intercept.

In this case, we are given the slope (2) and the y-intercept (-3).

y=2x-3

Good luck,

Paul

Posted on Dec 06, 2017

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Posted on Jan 02, 2017

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Posted on May 20, 2015

SOURCE: A line with a slope of 1 passes through the point 4, 8.What is its equation in slope-intercept form?

2- 4 - 8 - 16

Posted on Nov 03, 2015

that sounds like a problem about "slopes" so I am looking at using the derivative, which is basically the slope of the graph.

- the equation of line PQ can be simplified to y(x) = -2kx + k -8

- derivative relative to X (k is a constant) gives you -2k

- derivative of y(x) = 4x + 7 relative to x gives you 4

if the lines are parallel then the slopes are equal:

-2k=4 gives you k = -2 => your function becomes y = 4x - 8

if the lines are perpendicular the two slopes multiplied together give you -1:

-2k * 4 = -1 gives you k=1/8 => function becomes y = -1/4x - 7/8 or in other words y = -(2x+7)/8

I have made graphic representation and it looks to be correct.

I hope it makes sense.

- the equation of line PQ can be simplified to y(x) = -2kx + k -8

- derivative relative to X (k is a constant) gives you -2k

- derivative of y(x) = 4x + 7 relative to x gives you 4

if the lines are parallel then the slopes are equal:

-2k=4 gives you k = -2 => your function becomes y = 4x - 8

if the lines are perpendicular the two slopes multiplied together give you -1:

-2k * 4 = -1 gives you k=1/8 => function becomes y = -1/4x - 7/8 or in other words y = -(2x+7)/8

I have made graphic representation and it looks to be correct.

I hope it makes sense.

Apr 12, 2017 | Homework

I think you are missing some information in the question. Please provide the complete question.

Apr 12, 2017 | Homework

It's a vertical line so the slope is infinite.

Mar 29, 2017 | Homework

Lots and lots and lots. When you think the angle is nearly 180 degrees or a straight line, it must have lots and lots of sides.

The total of the interior angles of a polygon is given by (n-2)180, so the angle of each interior angle of a regular polygon is given by ((n-2)180)/n.

Now we set this to be equal to 176 and solve for n.

(n-2)180 = 176

-----------

n

Multiplying both sides by n, we get (n-2) 180 = 176n

Expanding the left side of the equation, 180n - 360 = 176n

Subtracting 176n from both sides and adding 360 to both sides, we get

180n - 176n = 360

4n = 360

Dividing both sides by 4, n = 90

Thus, you need a regular polygon of 90 sides to get an internal angle of 176 degrees.

Hopefully you don't have to construct it.

Good luck,

Paul

The total of the interior angles of a polygon is given by (n-2)180, so the angle of each interior angle of a regular polygon is given by ((n-2)180)/n.

Now we set this to be equal to 176 and solve for n.

(n-2)180 = 176

-----------

n

Multiplying both sides by n, we get (n-2) 180 = 176n

Expanding the left side of the equation, 180n - 360 = 176n

Subtracting 176n from both sides and adding 360 to both sides, we get

180n - 176n = 360

4n = 360

Dividing both sides by 4, n = 90

Thus, you need a regular polygon of 90 sides to get an internal angle of 176 degrees.

Hopefully you don't have to construct it.

Good luck,

Paul

Mar 26, 2017 | Homework

Lots and lots and lots. When you think the angle is nearly 180 degrees or a straight line, it must have lots and lots of sides.

The total of the interior angles of a polygon is given by (n-2)180, so the angle of each interior angle of a regular polygon is given by ((n-2)180)/n.

Now we set this to be equal to 176 and solve for n.

(n-2)180 = 176

-----------

n

Multiplying both sides by n, we get (n-2) 180 = 176n

Expanding the left side of the equation, 180n - 360 = 176n

Subtracting 176n from both sides and adding 360 to both sides, we get

180n - 176n = 360

4n = 360

Dividing both sides by 4, n = 90

Thus, you need a regular polygon of 90 sides to get an internal angle of 176 degrees.

Hopefully you don't have to construct it.

Good luck,

Paul

The total of the interior angles of a polygon is given by (n-2)180, so the angle of each interior angle of a regular polygon is given by ((n-2)180)/n.

Now we set this to be equal to 176 and solve for n.

(n-2)180 = 176

-----------

n

Multiplying both sides by n, we get (n-2) 180 = 176n

Expanding the left side of the equation, 180n - 360 = 176n

Subtracting 176n from both sides and adding 360 to both sides, we get

180n - 176n = 360

4n = 360

Dividing both sides by 4, n = 90

Thus, you need a regular polygon of 90 sides to get an internal angle of 176 degrees.

Hopefully you don't have to construct it.

Good luck,

Paul

Mar 26, 2017 | Homework

slope or m = (y2 -y1)/(x2-x1)

always start with the same point.

m = (1 - (-5))/(-2-5)

m = (1 + 5)/(-7)

m = 6/-7

m = -6/7

The y-intercept is the b in the equation y=mx+b.

We can use either point to calculate b. Let's use (-2,1). So every time we see x, we put in -2, and every time we see y, we put in 1.

y = -6/7x + b

1 = -6/7 (-2) + b

1 = 12/7 + b

1 = 1 5/7 + b

-5/7 = b

So, y = -6/7x - 5/7

To check, we substitute in the other point and see if the left side is equal to the right side.

LS RS

-5 -6/7(5) - 5/7

-5 -30/7 - 5/7

-5 -35/7

-5 -5

LS = RS

QED

Good luck,

Paul

always start with the same point.

m = (1 - (-5))/(-2-5)

m = (1 + 5)/(-7)

m = 6/-7

m = -6/7

The y-intercept is the b in the equation y=mx+b.

We can use either point to calculate b. Let's use (-2,1). So every time we see x, we put in -2, and every time we see y, we put in 1.

y = -6/7x + b

1 = -6/7 (-2) + b

1 = 12/7 + b

1 = 1 5/7 + b

-5/7 = b

So, y = -6/7x - 5/7

To check, we substitute in the other point and see if the left side is equal to the right side.

LS RS

-5 -6/7(5) - 5/7

-5 -30/7 - 5/7

-5 -35/7

-5 -5

LS = RS

QED

Good luck,

Paul

Mar 23, 2017 | Homework

5x+3=43

Mar 22, 2017 | Homework

Let's rewrite as

7(3x+5) = 8x -1(1-4x)

Let's distribute

21x + 35 = 8x -1 + 4x

collect like terms

21x + 35 = 12x -1

Put all the x's on one side by subtracting 12x from both sides

21x -12x + 35 = 12x -1 -12x

simplify

9x + 35 = -1

get all the constants on the right side

9x + 35 - 35 = -1 - 35

9x = -36

divide both sides by 9 to get x by itself

9x /9 = -36/9

x = -4

check in original equation

7(3(-4)+5) = 8(-4) -(1-4(-4))

7(-12+5) = -32 - (1+16)

7 (-7) = -32 - (17)

-49 = -32-17

-49 = -49

7(3x+5) = 8x -1(1-4x)

Let's distribute

21x + 35 = 8x -1 + 4x

collect like terms

21x + 35 = 12x -1

Put all the x's on one side by subtracting 12x from both sides

21x -12x + 35 = 12x -1 -12x

simplify

9x + 35 = -1

get all the constants on the right side

9x + 35 - 35 = -1 - 35

9x = -36

divide both sides by 9 to get x by itself

9x /9 = -36/9

x = -4

check in original equation

7(3(-4)+5) = 8(-4) -(1-4(-4))

7(-12+5) = -32 - (1+16)

7 (-7) = -32 - (17)

-49 = -32-17

-49 = -49

Jan 04, 2017 | Homework

Feb 19, 2018 | Homework

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