Final answer:
To write and graph a direct variation equation that passes through a given point, use the form y = kx, where k is the constant of variation. Substitute the values of x and y from the given point into the equation to find the value of k. Graph the equation by plotting the given point and drawing a line that passes through it.
Step-by-step explanation:
To write and graph a direct variation equation, we need to use the form y = kx, where k is the constant of variation. To find the value of k, we can use the given point (5, -6).
Substituting the values of x and y into the equation, we get -6 = k(5). Solving for k, we have k = -6/5.
Therefore, the direct variation equation that passes through the point (5, -6) is y = -6/5 x. We can graph this equation by plotting the point (5, -6) and drawing a straight line that passes through that point.