Chapter 1.1, Problem 29E

To determine

To find: three additional points on a line with a given point and slope.

Answer to Problem 29E

Three possible points on the given line is $(1,-11),(-1,-7),(2,-13)$.

Explanation of Solution

Given Information:

The point in a line with slope $m=-2$ is $(0,-9)$ .

Formula used:

When the slope of the line and a point on the line is given, the equation of line can be obtained using the point-slope form as,

  $y-y_1=m(x-x_1)$ ............ (1)

The equation of a line is of the form $y=mx+c$ where m denotes the slope, $(x,y)$ denotes the x and y coordinates in the line and c is a constant. So, by choosing a value for $x=0,\pm 1,\pm \mathrm{2..}$the corresponding value of y can be obtained which gives the coordinates of different points on the line.

Calculation Substituting the given point $(0,-9)$ and slope $m=-2$ in (1), the equation of line can be found as,

  $\begin{array}{l}y-\left(-9\right)=-2(x-0)\\ y+9=-2x\\ y=-2x-9\end{array}$

Thus, the equation of the line is obtained. Now, three different points on the line can be found as follows.

Consider $x=1$ , Substituting it in the equation of the line,

  $\begin{array}{c}y=-2\left(1\right)-9\\ =-2-9\\ =-11\end{array}$

Thus, the point is $(1,-11)$ .

Now, consider $x=-1$ . Substituting it in the equation of the line gives,

  $\begin{array}{c}y=-2\left(-1\right)-9\\ =2-9\\ =-7\end{array}$

Thus, the coordinates of the point is $(-1,-7)$ .

Now, considering $x=2$ , Substituting it in the equation of the line gives,

  $\begin{array}{c}y=-2\left(2\right)-9\\ =-4-9\\ =-13\end{array}$

Thus, the coordinates of the point is $(2,-13)$ .