Simplify the equation if possible. Find the \( x \)-intercept and the \( y \)-intercept. Then graph the equation \( -4 x-3 y=6 \)

To simplify the equation \( -4x - 3y = 6 \), we can rewrite it in slope-intercept form (y = mx + b). Add \( 4x \) to both sides: \(-3y = 4x + 6\). Then, divide every term by \(-3\): \(y = -\frac{4}{3}x - 2\). To find the \( x \)-intercept, set \( y = 0 \): \(0 = -\frac{4}{3}x - 2\) leads to \(x = -\frac{3}{2}\). For the \( y \)-intercept, set \( x = 0 \): \(y = -\frac{4}{3}(0) - 2 = -2\). So, the \( x \)-intercept is \((-1.5, 0)\) and the \( y \)-intercept is \((0, -2)\). When you graph it, plot the \( x \)- and \( y \)-intercepts and draw a line through them to visualize the linear relationship! 🎨📈 Remember, parallel lines have the same slope but different intercepts, while perpendicular lines have slopes that are negative reciprocals of each other. Engaging with different slopes can provide visual insights into these concepts. Additionally, you may want to consider how real-world problems can often be modeled with linear equations, such as budgeting scenarios where you might track income (x) and expenses (y). Understanding the relationship between these variables can help you make better financial decisions! 💸💼