Final answer:
To find the equation of a line that is perpendicular to the given line and passes through the point (14, -14), we need to determine the slope of the given line first. The equation of the perpendicular line is y = (4/3)x - 56/3.
Step-by-step explanation:
To find the equation of a line that is perpendicular to the given line and passes through the point (14, -14), we need to determine the slope of the given line first. The given line is 1 - (8y + 6x)/2 = 4, which can be simplified to 8y + 6x = -6. The slope of this line can be found by rearranging the equation in the form y = mx + b, where m is the slope. In this case, the equation becomes y = -3/4x - 1.
To find the slope of the line perpendicular to this line, we can use the fact that the product of the slopes of two perpendicular lines is -1. Therefore, the slope of the perpendicular line is 4/3.
Using the point-slope form of a linear equation, y - y1 = m(x - x1), we can substitute the values of the given point (14, -14) and the slope 4/3 into the equation to find the equation of the perpendicular line.
So the equation of the line perpendicular to the given line and passing through the point (14, -14) is y + 14 = (4/3)(x - 14), which can be simplified to y = (4/3)x - 56/3.