Final answer:
To find the equation of a line parallel to 4y - 3x = 12 and passing through the point (4, 0), we need to determine the slope of the given line and use the point-slope form of a line.
Step-by-step explanation:
To find the equation of a line parallel to 4y - 3x = 12 and passing through the point (4, 0), we need to determine the slope of the given line. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. We can rearrange the given equation to solve for y in terms of x: y = (3/4)x + 3. Comparing this equation to the slope-intercept form, we can see that the slope of the given line is 3/4.
Since we want a line parallel to this one, it will have the same slope of 3/4. Now, we can use the point-slope form of a line, which is y - y₁ = m(x - x₁). Plugging in the coordinates of the given point (4, 0) and the slope 3/4, we get the equation y - 0 = (3/4)(x - 4). Simplifying, y = (3/4)x - 3.
Therefore, the equation of the line parallel to 4y - 3x = 12 and passing through the point (4, 0) is y = (3/4)x - 3.