Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The graph showrs the proportional relationship. Derive the equation of the line $\newline$ $y=mx$ through the origin. $\newline$ ( $1$ point)

View step-by-step help

View step-by-step help

Find derivatives of exponential functions

Full solution

Q. The graph showrs the proportional relationship. Derive the equation of the line

\newline

y=mx

through the origin.

\newline

(

1

point)

Understand the Problem: Understand the problem. $\newline$ We need to find the equation of a line that passes through the origin and has a proportional relationship between $y$ and $x$ , which means $y$ is directly proportional to $x$ .
Point-Slope Form: Use the point-slope form of a line's equation. The point-slope form is $y - y_1 = m(x - x_1)$ , where $(x_1, y_1)$ is a point on the line and $m$ is the slope. Since the line passes through the origin, $(x_1, y_1)$ is $(0, 0)$ .
Substitute Origin: Substitute the origin into the point-slope form. $\newline$ Substituting $(0, 0)$ into the equation gives us $y - 0 = m(x - 0)$ , which simplifies to $y = mx$ .
Verify Equation: Verify the equation. $\newline$ The equation $y = mx$ represents a line passing through the origin with a slope of $m$ , which is what we were looking for.

More problems from Find derivatives of exponential functions

Question

\lim_{\theta \rightarrow \frac{\pi}{2}} \tan ^{2}(\theta)[1-\sin (\theta)]

\newline

1

\newline

0

\newline

\frac{1}{2}

\newline

-2

\newline

(D) The limit doesn't exist

Posted 3 months ago

Question

\lim _{\theta \rightarrow \frac{\pi}{2}} \frac{\sin ^{2}(2 \theta)}{1-\sin ^{2}(\theta)}

\newline

1

\newline

1

\newline

2

\newline

4

\newline

(D) The limit doesn't exist

Posted 3 months ago

Question

\lim _{x \rightarrow 3} \frac{x-3}{\sqrt{4 x+4}-4}

\newline

1

\newline

-4

\newline

1

\newline

2

\newline

(D) The limit doesn't exist

Posted 3 months ago

Question

\lim _{x \rightarrow-4} \frac{7 x+28}{x^{2}+x-12}

\newline

1

\newline

1

\newline

7

\newline

-1

\newline

(D) The limit doesn't exist

Posted 3 months ago

Question

\lim _{x \rightarrow-3} \frac{x+3}{4-\sqrt{2 x+22}}

\newline

1

\newline

-3

\newline

-4

\newline

-\frac{3}{4}

\newline

(D) The limit doesn't exist

Posted 3 months ago

Question

\lim _{x \rightarrow 1} \frac{\sqrt{5 x+4}-3}{x-1}

\newline

1

\newline

\frac{3}{5}

\newline

\frac{5}{6}

\newline

1

\newline

(D) The limit doesn't exist

Posted 3 months ago

Question

\lim _{x \rightarrow-2} \frac{x^{3}+3 x^{2}+2 x}{x+2}

\newline

1

\newline

6

\newline

0

\newline

2

\newline

(D) The limit doesn't exist

Posted 3 months ago

Question

\lim _{x \rightarrow \frac{\pi}{2}} \frac{\cot ^{2}(x)}{1-\sin (x)}

\newline

1

\newline

-1

\newline

-\frac{\pi}{2}

\newline

2

\newline

(D) The limit doesn't exist

Posted 3 months ago

Question

\lim _{x \rightarrow \frac{\pi}{2}} \frac{\sin (2 x)}{\cos (x)}

\newline

1

\newline

\frac{1}{2}

\newline

1

\newline

2

\newline

(D) The limit doesn't exist

Posted 3 months ago

Question

\lim _{\theta \rightarrow \frac{\pi}{4}} \frac{\cos (2 \theta)}{\sqrt{2} \cos (\theta)-1}

\newline

1

\newline

2

\newline

\frac{1}{2}

\newline

\sqrt{2}

\newline

(D) The limit doesn't exist

Posted 3 months ago