Chapter 1.5, Problem 1CFU

To determine

To describe: that two lines are parallel or coincide by looking at equations of line in standard form.

Answer to Problem 1CFU

Two parallel lines have same slope. Put values of A and B in $m=-\frac{A}{B}$ to check whether they are equal.

For coinciding lines: The two lines have same slope and y-intercept. Put values of A and B in $m=-\frac{A}{B}$ to check whether they are equal. Then put the values of A and B in $b=-\frac{C}{B}$ to check whether they are equal.

Explanation of Solution

Given information:

Standard form of line is as follows:

  $Ax+By+C=0$

Calculation Equation for slope of line is as follows:

  $m=-\frac{A}{B}$ … (1)

Equation for y-intercept of line is as follows:

  $b=-\frac{C}{B}$ … (2)

For parallel lines: The two lines have same slope. Put values of A and B in equation (1) to check whether they are equal.

For coinciding lines: The two lines have same slope and y-intercept. Put values of A and B in equation (1) to check whether they are equal. Then put the values of A and B in equation (2) to check whether they are equal.