Questions About How To Find Slope

Betty asks…

How do you find slope intercept form for this line?

I need to find slope intercept form for a line passing through the point (5,8) and perpendicular to the line passing through the points (-8,7) and (-2,0).
Do you find the slope of the line passing through (-8,7) and then flip the slope?

admin answers:

Step 1: Find the slope of the perpendicular line passing thru (-8,7) (-2,0). Use point-slope formula:

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

. . = (7 - 0) / (-8 - (-2))

. . = 7 / (-8 + 2)

. . = 7 / - 6


Step 2: Get the slope of the line passing thru (5, 8) by flipping the above slope, and multiply by -1.

M = (- 6 / 7) * -1

. . = 6 / 7


Step 3: Use the point slope formula again to get the slope intercept form equation. Plug in what you know. Then solve for y.

M = (y1 - y2) / (x1 - x2)

6 / 7 = (8 - y)(5 - x)


Cross multiply

6(5 - x) = 7(8 - y)

30 - 6x = 56 - 7y

- 6x = 26 - 7y

- 6x + 7y = 26

7y = 26 + 6x

y = 26/7 + 6/7 x


Rearrange to get

y = 6/7 x + 26/7

Carol asks…

How to find function domains, and help finding slope of aline?

I'm having trouble finding the domain of functions. Could someone kindly explain how to get the domains of these functions to me;

Question 1:
f(x) = x^2 - 9

Question 2:
f(x) = | 48 - x |

Question 3:
f(x) = 8
------
x + 9

Does Question 3 equal x is a real number and x cannot equal -9?



Also I had a quick question regarding the slope of a line. I found the slope but it equals -10.5/20 do I divide from there to find the slope because then it would give me -0.525 and for some reason that doesn't look right to me.

admin answers:

1. All Real
2. All Real
3. X cannot be -9

You need to post the full question so I can help.

Joseph asks…

How to make a program to find slope and y-intercept of an equation for ti-83 calculator?

I'm trying to find M (slope) & B (y-intercept) of my equation by using a program. How do I do this??? Please help. Thanks.

admin answers:

You don't specify what your inputs are. If there are no given values, there's no way to calculate slope or a y-intercept based on no information.

Charles asks…

Find slope of the tangent line of the graph at a specific point?

Find the slope of the tangent line of the graph of f(x) = √(5x^2+4) (all under square root) at the point where x = -1
I know how to start it, but I cannot get to the answer! Please help.

admin answers:

Use the chain rule to differentiate this function. The chain rule is dy/dx = dy/du * du/dx where u is a function of x. I am using y instead of f(x).

Let u = 5x^2 + 4....................then du/dx = 10x

Let y = sqrt(u) = u^(1/2).........then dy/du = (1/2) * u^(-1/2) = (1 / sqrt(u)) =
(from the definition of u) (1 / sqrt(5x^2 + 4))

So dy/dx = (1 / sqrt(5x^2 + 4)) * 10x = (10x / sqrt(5x^2 + 4)

Where x = -1, dy/dx = ((10 * (-1)) / (sqrt(5 + 4)) = (-10 / 3)

Now we need to know the value of y where x = -1. Y = sqrt(5 + 4) = 3

So the tangent line has a slope of m = (-10 / 3) and passes through (-1,3)

y = (-10 / 3) * x + b (where b is an unknown constant).

Since this line passes through (-1,3), Substitute -1 for x and 3 for y into the above equation.

3 = ((-10 / 3) * -1) + b = +(10 / 3) + b

Subtract (10 / 3) from both sides of this equation.

3 - (10/3) = b

b = (/3) - (10/3) = (-1/3)

So the tangent line is y = ((-10 / 3) * x) - (1/3) <-------------- Answer

.

Mary asks…

How to find slope-intercept equation when given the slope and x-intercept?

Slope-intercept equation:
y=mx+b

How do you find the equation, when you are giving the slope and the x-intercept (instead of the y-intercept)?

For example, the slope is 3.0 and the x-intercept is (-2,0).

admin answers:

You can take the point-slope form of a line

(y-0) = 3 (x - (-2))

and solve it for y.

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