Final Answer:
The equation 2x + 3y = k represents a line parallel to the line 2x + 3y = 24, where k is any constant value.
Explanation:
In order for two lines to be parallel, they must have the same slope. The slope of a line is determined by the coefficient of the x-term in the equation. In the given equation, the coefficient of x is 2. Therefore, the slope of this line is 2.
To find the equation of a parallel line, we can use the slope-intercept form of a line, y = mx + b, where m represents the slope and b represents the y-intercept. Since we know that the slope of the parallel line is 2, we can plug in this value for m. Now we have the equation y = 2x + b.
To find the value of b, we need to use the fact that the parallel line passes through the same point as the given line. The given line has the point (0,8) on it. This means that when x = 0, y = 8. Plugging these values into our equation, we get 8 = 2(0) + b. Solving for b, we get b = 8.
Therefore, the equation of a line parallel to 2x + 3y = 24 is y = 2x + 8. This equation can also be written as 2x + 3y = k, where k is any constant value. This is because any equation with the same slope and y-intercept will be parallel to the given line.
In conclusion, the equation 2x + 3y = k represents a line parallel to the line 2x + 3y = 24, where k is any constant value. By using the slope-intercept form and the fact that parallel lines have the same slope, we can easily determine the equation of a parallel line.