20) through: (-1,-3) perp.to y=-(5)/(3)x-4 A) y=-(12)/(5)x+(3)/(5) B) y=-(3)/(5)x-(12)/(5) C) y=(2)/(5)x-(12)/(5) D) y=(3)/(5)x-(12)/(5)

To find the equation of the line that passes through the point $(-1,-3)$ and is perpendicular to the line $y=-\frac{5}{3}x-4$, we need to determine the slope of the perpendicular line.<br /><br />The slope of the given line $y=-\frac{5}{3}x-4$ is $-\frac{5}{3}$. The slope of a line perpendicular to this line is the negative reciprocal of $-\frac{5}{3}$, which is $\frac{3}{5}$.<br /><br />Now, we can use the point-slope form of a linear equation to find the equation of the perpendicular line. The point-slope form is given by:<br /><br />$y - y_1 = m(x - x_1)$<br /><br />where $(x_1, y_1)$ is a point on the line and $m$ is the slope.<br /><br />Substituting the point $(-1,-3)$ and the slope $\frac{3}{5}$ into the point-slope form get:<br /><br />$y - (-3) = \frac{3}{5}(x - (-1))$<br /><br />Simplifying this equation, we have:<br /><br />$y + 3 = \frac{3}{5}(x + 1)$<br /><br />$y + 3 = \frac{3}{5}x + \frac{3}{5}$<br /><br />$y = \frac{3}{5}x + \frac{3}{5} - 3$<br /><br />$y = \frac{3}{5}x - \frac{12}{5}$<br /><br />Therefore, the equation of the line that passes through the point $(-1,-3)$ and is perpendicular to the line $y=-\frac{5}{3}x-4$ is $y = \frac{3}{5}x - \frac{12}{5}$.<br /><br />The correct answer is D) $y = \frac{3}{5}x - \frac{12}{5}$.