Chapter 1.1, Problem 28E

To determine

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

Answer to Problem 28E

Three possible points on the given line are $\left(-4,0\right),\left(-4,1\right)and\left(-4,-1\right)$

Explanation of Solution

Given Information:

The point on a line with undefined slope is $\left(-4,1\right)$ .

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

Calculation An undefined slope can be expressed as $m=\frac{1}{0}$

Substituting the given point $\left(-4,1\right)$ and slope in (1), the equation of line can be found as,

  $\begin{array}{l}y-\left(1\right)=\frac{1}{0}(x-\left(-4\right))\\ 0=x+4\\ x=-4\end{array}$

Thus, the equation of the line is obtained. This represents a vertical line parallel to the y-axis and represents a constant value.

Here, the x -value remains constant and it consists of all possible y -values.

Three possible points are $\left(-4,0\right),\left(-4,1\right)and\left(-4,-1\right)$ .