Find the slope and the \( y \)-intercept of the line. \[ -9 x-3 y=-4 \] Write your answers in simplest form. slope: \( y \)-intercept: -1

To find the slope and \( y \)-intercept of the line given by the equation \( -9x - 3y = -4 \), we need to rearrange it into the slope-intercept form \( y = mx + b \). First, isolate \( y \): \[ -3y = 9x - 4 \] Now divide by -3: \[ y = -3x + \frac{4}{3} \] From this form, the slope \( m \) is -3, and the \( y \)-intercept \( b \) is \( \frac{4}{3} \), not -1 as stated. Learning about the history of linear equations reveals that they date back to ancient civilizations, including the Babylonians and Egyptians, who solved linear equations for practical matters like trade and construction. The systematic approach we use today began to form in the 17th century with the advent of algebra and coordinate geometry. When dealing with lines in a coordinate plane, it's common to make mistakes by misinterpreting the slope as the rise over the run. Always remember, the slope \( m \) indicates how steep the line is, and it tells you how much \( y \) changes for a given change in \( x \). A common pitfall is forgetting to change the sign when dividing or moving terms from one side of the equation to another!