What is an equation of the line that passes through the point (-5,-7) and is parallel to the line 3x-5y=10 Answer Attemptiout of square

To find the equation of the line that passes through the point $(-5,-7)$ and is parallel to the line $3x-5y=10$, we need to follow these steps:<br /><br />1. Find the slope of the given line $3x-5y=10$.<br />2. Use the slope and the given point to find the equation of the parallel line.<br /><br />Step 1: Find the slope of the given line $3x-5y=10$.<br /><br />To find the slope, we need to rewrite the equation in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.<br /><br />$3x - 5y = 10$<br />$-5y = -3x + 10$<br />$y = \frac{3}{5}x - 2$<br /><br />The slope of the given line is $\frac{3}{5}$.<br /><br />Step 2: Use the slope and the given point to find the equation of the parallel line.<br /><br />Since the parallel line has the same slope as the given line, the slope of the parallel line is also $\frac{3}{5}$.<br /><br />Now, we can use the point-slope form of a linear equation to find the equation of the parallel line. The point-slope form 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 />Using the given point $(-5,-7)$ and the slope $\frac{3}{5}$, we have:<br /><br />$y - (-7) = \frac{3}{5}(x - (-5))$<br />$y + 7 = \frac{3}{5}(x + 5)$<br /><br />To simplify the equation, we can multiply both sides by 5 to eliminate the fraction:<br /><br />$5(y + 7) = 3(x + 5)$<br />$5y + 35 = 3x + 15$<br /><br />Finally, we can rearrange the equation to get it in slope-intercept form:<br /><br />$3x - 5y = 20$<br /><br />Therefore, the equation of the line that passes through the point $(-5,-7)$ and is parallel to the line $3x-5y=10$ is $3x - 5y = 20$.