Chapter 4.2, Problem 20PPS

To determine

The equation in point slope form, slope-intercept form and standard form for line with slope -3 and coordinate (-2, 6).

Answer to Problem 20PPS

The equation in point slope form, slope-intercept form and standard form are $y-6=-3\left(x+2\right)$ , $y=-3x+0$ and $3x+y=0$ respectively.

Explanation of Solution

Given:

The line has slope -3 and coordinate (-2, 6).

Calculation:

Point slope form of line is expressed as follows:

  $y-y_1=m\left(x-x_1\right)$

Here, m is slope.

Substitute the slope and coordinate in the point slope form as follows:

  $\begin{array}{l}y-6=-3\left(x-\left(-2\right)\right)\\ y-6=-3\left(x+2\right)\end{array}$

Thus, the point-slope form of line is $y-6=-3\left(x+2\right)$ .

Standard form is calculated as follows:

  $\begin{array}{l}y-6=-3\left(x+2\right)\\ y-6=-3x-6\\ 3x+y=0\end{array}$

Thus, the standard equation of line is $3x+y=0$ .

Slope-intercept form is calculated as follows:

  $\begin{array}{l}3x+y=0\\ y=-3x+0\end{array}$

Thus, the slope-intercept form of line is $y=-3x+0$ .