Chapter 1.1, Problem 1E

To determine

To match: The equations to its form.

Answer to Problem 1E

  $\begin{array}{l}\left(a\right)Ax+By+C=0\to \left(\text{iii}\right)\text{ general form,}\left(b\right)x=a\to \left(\text{i}\right)\text{ vertical line,}\left(c\right)y=b\to \left(\text{v}\right)\text{ horizontal line,}\\ \left(d\right)y=mx+b\to \left(\text{ii}\right)\text{ slope - intercept form,}\left(e\right)y-y_1=m\left(x-x_1\right)\to \left(\text{iv}\right)\text{ point - slope form}\end{array}$

Explanation of Solution

Given information:

Given equations are,

  $\begin{array}{l}\left(a\right)Ax+By+C=0\\ \left(b\right)x=a\\ \left(c\right)y=b\\ \left(d\right)y=mx+b\\ \left(e\right)y-y_1=m\left(x-x_1\right)\end{array}$

Given forms are,

  $\begin{array}{l}\left(\text{i}\right)\text{ vertical line}\\ \left(\text{ii}\right)\text{ slope - intercept form}\\ \left(\text{iii}\right)\text{ general form}\\ \left(\text{iv}\right)\text{ point - slope form}\\ \left(\text{v}\right)\text{ horizontal line}\end{array}$

General equation of the line is $Ax+By+C=0$

Vertical line is $x=a$

Horizontal line is $y=b$

Slope intercept form of the line is $y=mx+b$

Point − slope form of the line is $y-y_1=m\left(x-x_1\right)$

Therefore, the correct matching is,

  $\begin{array}{l}\left(a\right)Ax+By+C=0\to \left(\text{iii}\right)\text{ general form,}\left(b\right)x=a\to \left(\text{i}\right)\text{ vertical line,}\left(c\right)y=b\to \left(\text{v}\right)\text{ horizontal line,}\\ \left(d\right)y=mx+b\to \left(\text{ii}\right)\text{ slope - intercept form,}\left(e\right)y-y_1=m\left(x-x_1\right)\to \left(\text{iv}\right)\text{ point - slope form}\end{array}$