Answer: y = -\frac{3}{5}x + \frac{67}{5}$ or -3/5x + 67/5
Explanation:
To find the equation of a line that is perpendicular to a given line, we need to find the slope of the given line, then negate the reciprocal of that slope. The equation of the line with slope $m$ and passing through the point $(x_1, y_1)$ is given by:
$$y - y_1 = m(x - x_1)$$
In our case, we can find the slope of the given line $5x - 3y = 21$ by writing it in slope-intercept form, which is $y = \frac{5}{3}x - \frac{21}{3}$. The slope of this line is $\frac{5}{3}$, so the slope of the line perpendicular to it is $-\frac{3}{5}$.
We also know that the line passes through the point $(5, 8)$, so we can plug these values into the equation for a line with slope $m$ and point $(x_1, y_1)$ to get:
$$y - 8 = -\frac{3}{5}(x - 5)$$
This simplifies to $y = -\frac{3}{5}x + \frac{67}{5}$, so the equation of the line perpendicular to the given line and passing through the point $(5, 8)$ is $y = -\frac{3}{5}x + \frac{67}{5}$.