Chapter 4.1, Problem 57PPS

To determine

To find:The equation of a line that passes through the origin and has a slope of 3.

Answer to Problem 57PPS

The equation of the line is $y=3x$ .

Explanation of Solution

Given:

The line passes through the origin $\left(0,0\right)$ .

The slope of the line is $m=3$

Calculation:

The line passing through the point $\left(0,0\right)$ . The line has the slope of 3.

The equation of the line can be written as $y=3x$

The standard form of point and slope form of the equation is $y-y_1=m\left(x-x_1\right)$ .

Here, $\left(x_1,y_1\right)$ is the point through which the line passes.

Substitute $\left(0,0\right)$ for $\left(x_1,y_1\right)$ and $m=3$ .

The equation of the line is

  $\begin{array}{l}y-0=3\left(x-0\right)\\ y=3x\end{array}$

Plot this equation on the Cartesian plane. Then plot clearly shows the line.

  

Therefore, the equation of the line is $y=3x$ .