What is an equation of the line that passes through the point (-5,-3) and is perpendicular to the line 5x-3y=18 Answer Attempt 1 out of 2 square

To find the equation of the line that passes through the point $(-5,-3)$ and is perpendicular to the line $5x-3y=18$, we need to follow these steps:<br /><br />1. Find the slope of the given line $5x-3y=18$.<br />2. Find the slope of the line perpendicular to the given line.<br />3. Use the point-slope form of a linear equation to find the equation of the perpendicular line.<br /><br />Step 1: Find the slope of the given line $5x-3y=18$.<br />To find the slope of the given line, we need to rewrite it in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.<br /><br />$5x-3y=18$<br />$-3y = -5x + 18$<br />$y = \frac{5}{3}x - 6$<br /><br />The slope of the given line is $\frac{5}{3}$.<br /><br />Step 2: Find the slope of the line perpendicular to the given line.<br />The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.<br /><br />The slope of the given line is $\frac{5}{3}$, so the slope of the perpendicular line is $-\frac{3}{5}$.<br /><br />Step 3: Use the point-slope form of a linear equation to find the equation of the perpendicular line.<br />The point-slope form of a linear equation is $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope.<br /><br />We are given the point $(-5,-3)$ and the slope $-\frac{3}{5}$, so we can substitute these values into the point-slope form:<br /><br />$y - (-3) = -\frac{3}{5}(x - (-5))$<br />$y + 3 = -\frac{3}{5}(x + 5)$<br /><br />Now, we can simplify this equation:<br /><br />$y + 3 = -\frac{3}{5}x - 3$<br />$y = -\frac{3}{5}x - 6$<br /><br />Therefore, the equation of the line that passes through the point $(-5,-3)$ and is perpendicular to the line $5x-3y=18$ is $y = -\frac{3}{5}x - 6$.