Find the slope of the line. \( 6 x-5 y=10 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is (Type an integer or a simplified fraction.) B. The slope is undefined.

To find the slope of the line given by the equation \( 6x - 5y = 10 \), we can rearrange it into slope-intercept form (\( y = mx + b \)), where \( m \) is the slope. Start by isolating \( y \): 1. Subtract \( 6x \) from both sides: \(-5y = -6x + 10\) 2. Divide every term by \(-5\): \(y = \frac{6}{5}x - 2\) Now the equation is in the form \(y = mx + b\), where \(m = \frac{6}{5}\). A. The slope is \( \frac{6}{5} \). When analyzing the line's characteristics, also keep in mind that a slope represents the steepness of the line. If you have a positive slope like \( \frac{6}{5} \), it means the line rises as you move from left to right, which can visually be a fun way to understand how steep different lines can be in real life! You might consider how this slope compares to other lines, like a vertical line which has an undefined slope. Imagine pouring water down a staircase vs. a wall: the staircase (with a slope) channels the water smoothly, while the wall (undefined slope) leaves it to drop straight down!