The equation of a line is given below. \[ -3 x+4 y=-16 \] Find the slope and the \( y \)-intercept. Then use them to graph the line.

To find the slope and \( y \)-intercept of the equation \( -3x + 4y = -16 \), we first need to rearrange it into slope-intercept form, which is \( y = mx + b \). Starting with the given equation: 1. Add \( 3x \) to both sides: \( 4y = 3x - 16 \). 2. Divide all terms by 4: \( y = \frac{3}{4}x - 4 \). From this, the slope \( m \) is \( \frac{3}{4} \), and the \( y \)-intercept \( b \) is \( -4 \), meaning the line crosses the \( y \)-axis at \( (0, -4) \). To graph the line, start at the point \( (0, -4) \), then use the slope \( \frac{3}{4} \): - From \( (0, -4) \), move up 3 units and right 4 units to plot the next point at \( (4, -1) \). - Connect these points, and you'll have a perfectly straight line! Graphing lines isn't just useful in math; it's a foundational skill for fields like physics and economics! Whether you're analyzing trends in data or plotting a trajectory, being able to visualize relationships through graphs can help you convey information succinctly and effectively. For anyone looking to deepen their understanding of linear equations, consider exploring the concepts of intercepts, slope, and how they apply to different real-world scenarios, like predicting costs or analyzing motion. Books like "Algebra for Dummies" or online platforms like Khan Academy can offer great insights and resources!