Chapter 0.1, Problem 21E

To determine

To determine the point-slope equation of the line through the point $P\left(0,3\right)$ with slope $m=2$ .

Answer to Problem 21E

The point-slope equation of the line passing through the point $P\left(0,3\right)$ with slope $m=2$ :

  $y=3+2\left(x-0\right)$ .

Explanation of Solution

Given:

Given the slope of the line:

  $m=2$ .

Given a point $P$ through which the line passes:

  $P\left(0,3\right)$ .

Concept Used:

Point-Slope equation of a line:

Given the slope $m$ of a line and a point $P\left(x_1,y_1\right)$ through which the line passes, the Point-Slope equation of the line is as follows:

  $y=y_1+m\left(x-x_1\right)$ .

Calculation:

It is given that the line has the slope $m=2$ and that it passes through the point $P\left(x_1,y_1\right)=P\left(0,3\right)$ .

Then, the point-slope equation of the line is obtained by substituting $m=2$ and $\left(x_1,y_1\right)=\left(0,3\right)$ in the equation $y=y_1+m\left(x-x_1\right)$ .

Substitute $m=2$ and $\left(x_1,y_1\right)=\left(0,3\right)$ in the equation $y=y_1+m\left(x-x_1\right)$ :

  $y=3+2\left(x-0\right)$ .

Thus, the point-slope equation of the line passing through the point $P\left(0,3\right)$ with slope $m=2$ :

  $y=3+2\left(x-0\right)$ .

Conclusion:

The point-slope equation of the line passing through the point $P\left(0,3\right)$ with slope $m=2$ :

  $y=3+2\left(x-0\right)$ .