Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Complete the point-slope equation of the line through
(-4,8) and (4,4).
Use exact numbers.
y-4=◻

Complete the point-slope equation of the line through $(-4,8)$ and $(4,4)$ . $\newline$ Use exact numbers. $\newline$ $y-4=$ $\square$

View step-by-step help

View step-by-step help

Find equations of tangent lines using limits

Full solution

Q. Complete the point-slope equation of the line through

(-4,8)

and

(4,4)

.

\newline

Use exact numbers.

\newline

y-4=

\square

Find the slope: First, find the slope $m$ of the line using the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ where $(x_1, y_1)$ and $(x_2, y_2)$ are the given points. $\newline$ So, $m = \frac{4 - 8}{4 - (-4)}$
Calculate the slope: Now, calculate the slope: $m = \frac{-4}{8} = -\frac{1}{2}$ .
Use point-slope form: Next, use the point-slope form $y - y_1 = m(x - x_1)$ . We can use either point, but let's use $(4,4)$ . So, $y - 4 = \left(-\frac{1}{2}\right)(x - 4)$ .

More problems from Find equations of tangent lines using limits

Question

Consider the curve given by the equation

x y^{2}+5 x y=50

. It can be shown that

\frac{d y}{d x}=\frac{-y(y+5)}{x(2 y+5)} \text {. }

\newline

Write the equation of the vertical line that is tangent to the curve.

Posted 1 month ago

Question

The rate of change

\frac{d P}{d t}

of the number of algae in a tank is modeled by the following differential equation:

\newline

\frac{d P}{d t}=\frac{2317}{10614} P\left(1-\frac{P}{662}\right)

\newline

t=0

, the number of algae in the tank is

174

and is increasing at a rate of

28

algae per minute. At what value of

P

P(t)

growing the fastest?

\newline

Posted 2 months ago

Question

The rate of change

\frac{d P}{d t}

of the number of bacteria in a tank is modeled by the following differential equation:

\newline

\frac{d P}{d t}=\frac{2}{9849} P(598-P)

\newline

t=0

, the number of bacteria in the tank is

196

and is increasing at a rate of

16

bacteria per minute. At what value of

P

does the graph of

P(t)

have an inflection point?

\newline

Posted 2 months ago

Question

The rate of change

\frac{d P}{d t}

of the number of people infected by a disease is modeled by the following differential equation:

\newline

\frac{d P}{d t}=\frac{45}{125404} P(800-P)

\newline

t=0

, the number of people infected by the disease is

214

and is increasing at a rate of

45

people per hour. What is the limiting value for the total number of people infected by the disease as time increases?

\newline

Posted 2 months ago

Question

Which of the following is a correct interpretation of the expression

\newline

-4+13

\newline

1

\newline

(A) The number that is

4

-13

on the number line

\newline

(B) The number that is

4

to the right of

-13

on the number line

\newline

(C) The number that is

13

-4

on the number line

\newline

(D) The number that is

13

to the right of

-4

on the number line

Posted 2 months ago

Question

f

f(x)=x^{3}+2 \sin (3 x-3)

. Use a calculator to write the equation of the line tangent to the graph of

f

x=0.5

. You should round all decimals to

3

\newline

Posted 2 months ago

Question

f

f(x)=x^{2}-2 x+3 \cos \left(x^{2}-x\right)

. Use a calculator to write the equation of the line tangent to the graph of

f

x=-2.5

. You should round all decimals to

3

\newline

Posted 2 months ago

Question

f

f(x)=x^{2}+x-2 \sin (2 x)

. Use a calculator to write the equation of the line tangent to the graph of

f

x=3

. You should round all decimals to

3

\newline

Posted 2 months ago

Question

f

f(x)=x^{3}+\cos \left(2 x^{2}+5\right)

. Use a calculator to write the equation of the line tangent to the graph of

f

x=1

. You should round all decimals to

3

\newline

Posted 2 months ago

Question

f

f(x)=x^{3}+3-5 \sin \left(x^{2}\right)

. Use a calculator to write the equation of the line tangent to the graph of

f

x=1

. You should round all decimals to

3

\newline

Posted 2 months ago