Final answer:
The slope of a line perpendicular to the equation 14r + 8y = 12 is found by first rewriting the given equation in slope-intercept form to determine its slope and then using the negative reciprocal to find the perpendicular slope, which is 4/7.
Step-by-step explanation:
To find the slope of a line perpendicular to the given equation 14r + 8y = 12, we need to first express this equation in the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept. By rewriting the given equation, subtracting 14r from both sides and then dividing by 8, we get:
y = -14/8r + 12/8
y = -7/4r + 3/2
The slope (m) of this line is -7/4. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of a line perpendicular to the given line would be 4/7.
Therefore, the slope of a line perpendicular to the equation 14r + 8y = 12 is 4/7.