Solving the Linear Equation 5x + 6y = 0: Step-by-Step Guide

There are different methods to solve this equation, but one possible way is to solve for one of the variables in terms of the other, and then substitute that expression into the equation to obtain a simpler equation in one variable. For example:

5x + 6y = 0

Subtract 5x from both sides:

6y = -5x

Divide both sides by 6:

y = (-5/6)x

This means that y is a linear function of x with slope -5/6 and y-intercept 0. To graph this equation, we can plot any two points that satisfy it, such as (6,-5) and (12,-10), and then draw a straight line through them. Alternatively, we can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, and plug in the values we found:

y = (-5/6)x + 0

This is the equation of a line with slope -5/6 and y-intercept 0, which we can graph as follows:

First, plot the y-intercept (0,0). Then, use the slope to find another point. Since the slope is -5/6, we can move down 5 units (since it's negative) and to the right 6 units (since the denominator of the slope is 6). This gives us the point (6,-5). Finally, draw a straight line through the two points, which represents all the solutions to the equation.

The graph should look like this:

     |
     |
     |
     |       *
     |     /
     |   /
     | /
-----+------------->
     |  6  12  18  x
     |