We have that the linear equation is:
4x + 2y = 24
We need to convert this standard form of the line equation into the slope-intercept form of the line equation, that is, y = mx + b. Then, we can do as follows:
1. Subtract 4x from both sides of the equation:
2. Divide both sides of the equation by 2 (to isolate y):
Now, we have the slope-intercept form of the line equation. The slope, m, is m = -2.
Since we need to find a parallel line to this line, the new line needs to have the same slope, that is, m = -2.
Then, we have the slope, m = -2, and the point (6, 4). We can use the point-slope form of the line equation to find the parallel line. Therefore, we have:
And then, expanding this equation, we finally have that the parallel line is: