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enot [183]
3 years ago
8

Use the coordinates of the labeled point to find the point-slope equation of the line.

Mathematics
2 answers:
LenKa [72]3 years ago
6 0

For this case we have that by definition, the equation of a line of the point-slope form is given by:

y-y_ {0} = m (x-x_ {0})

Where:

m: It's the slope

(x_ {0}, y_ {0}): It is a point through which the line passes

To find the slope, we need two points through which the line passes, observing the image we have:

(x_ {1}, y_ {1}): (3, -5)\\(x_ {2}, y_ {2}): (0,4)\\m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {4 - (- 5)} {0-3} = \frac {4 + 5} {-3} = \frac {9} {- 3} = - 3

Thus, the equation is of the form:

y-y_ {0} = - 3 (x-x_ {0})

We choose a point:

(x_{0}, y_ {0}) :( 3, -5)

Finally, the equation is:

y - (- 5) = - 3 (x-3)\\y + 5 = -3 (x-3)

Answer:

y + 5 = -3 (x-3)

Option D

irina [24]3 years ago
3 0

Answer:

y + 5 = -3 (x-3)

Option D

Step-by-step explanation:

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notsponge [240]

Answer:

g(f(x)) = -x - 18

Step-by-step explanation:

2x - 6( (x + 6) / (2) )

2x - 3( x + 6)

2x - 3x - 18

-x - 18

4 0
3 years ago
Cressida decided to save a part of her income in a savings account that compounds interest every four months. Her account balanc
Bogdan [553]

Answer:

A

Step-by-step explanation:

account balance on compound interest = principal amount (1+rate/100)^time

here there are t years  so toat months are 12t and ad interest is after each 4 months so time is 12t/4 =3t

now total balance = 3545(1.045)^3t

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8 0
3 years ago
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A cone is sliced so the cross section is parallel to its base.
Alika [10]
The shape of the cross-section formed is a triangle, when a cone is cut in such a way that the cross-section is perpendicular to the base and it passes through the vertex.
3 0
3 years ago
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For the linear function f(x) = -2x+1 , find the following
Leya [2.2K]

Given:

The function is:

f(x)=-2x+1

To find:

a. Slope and Y-intercept.

b. Is the function increasing, decreasing, or constant, justify your answer.

c. Graph the function, label x, and y-intercepts.

Solution:

a. We have,

f(x)=-2x+1                  ...(i)

The slope intercept form of a line is:

y=mx+b                    ...(ii)

Where, m is the slope and b is the y-intercept.

On comparing (i) and (ii), we get

m=-2,b=1

Therefore, the slope of the line is -2 and the y-intercept is 1.

b. If the slope of a linear function is negative, then the function is decreasing.

If the slope of a linear function is positive, then the function is increasing.

If the slope of a linear function is 0, then the function is constant.

The slope of the linear function is negative.

Therefore, the function is decreasing.

c. We have,

f(x)=-2x+1

At x=0, we get

f(0)=-2(0)+1

f(0)=1

So, the y-intercept is at (0,1).

At f(x)=0, we get

0=-2x+1

2x=1

x=\dfrac{1}{2}

x=0.5

So, the x-intercept is at \left(0.5,0\right).

Plot the points (0,1), \left(0.5,0\right) and connect them by a straight line as shown below:

4 0
3 years ago
Can someone help me plzzzz with this math question!!!!!! “Buy one, get one free” special at T-Mobile for an iPhone 12. The cost
evablogger [386]

Answer:

$575

Step-by-step explanation

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