Find the slope of a line perpendicular to the line whose equation is x, minus, 6, y, equals, 24x−6y=24. Fully simplify your answer
To find the slope of a line perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line.
The given line's equation is 24x - 6y = 24. To simplify this equation, we can divide both sides by 6 to get the equation in slope-intercept form: 4x - y = 4. Rearranging the equation to isolate y, we have y = 4x - 4.
Now we can identify the slope of the given line. Since the equation is in slope-intercept form, we can see that the coefficient of x is the slope. Therefore, the slope of the given line is 4.
Now, to find the slope of a line perpendicular to this line, we need to find the negative reciprocal of 4. The negative reciprocal of a number is obtained by flipping the number and changing its sign.
Therefore, the negative reciprocal of 4 is -1/4.
Hence, the slope of a line perpendicular to the line whose equation is x-6y=24 is -1/4.