Final answer:
The slope of a line perpendicular to y=7/5x-4 is -5/7, found by taking the negative reciprocal of the original slope.
Step-by-step explanation:
To solve the mathematical problem completely, we need to find the slope of a line that is perpendicular to the given equation y=7/5x-4. The slope of any line is given by the coefficient of x in its equation when it's in the slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept.
The given line has a slope of 7/5. For a line to be perpendicular to another, its slope must be the negative reciprocal of the slope of the original line. Therefore, we go through the following steps:
- Take the negative reciprocal of 7/5, which is -5/7.
- This value, -5/7, is the slope of the line that is perpendicular to the given line.
The final answer is that the slope of the line perpendicular to y=7/5x-4 is -5/7.