Find the slope and \( y \)-intercept of the following linear equation. Express the \( y \)-intercept as a coordinate pair. \[ -2 x+10 y=-9 \] Answer

To find the slope and \( y \)-intercept of the equation \(-2x + 10y = -9\), we can rearrange it into the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\)-intercept. First, isolate \(y\): \[ 10y = 2x - 9 \] \[ y = \frac{2}{10}x - \frac{9}{10} \] \[ y = \frac{1}{5}x - \frac{9}{10} \] From this equation, the slope \(m\) is \(\frac{1}{5}\) and the \(y\)-intercept \(b\) is \(-\frac{9}{10}\). As a coordinate pair, the \(y\)-intercept is \((0, -\frac{9}{10})\). So, the slope is \(\frac{1}{5}\) and the \(y\)-intercept is \((0, -\frac{9}{10})\). If you're curious about the evolution of linear equations, they date back to ancient civilizations, where early mathematicians used geometric methods to solve linear problems long before algebra was developed. This laid the groundwork for future advancements in mathematics! In practical terms, knowing how to identify the slope and intercept of a linear equation is crucial in fields like economics, where it can help analyze trends, or in physics, to understand motion. You can quickly sketch graphs and make predictions based on these values, turning abstract math into real-world insights!