What is an equation of the line that passes through the points \( (4,-3) \) and \( (2,0) \) ?

To find the equation of the line passing through the points \((4, -3)\) and \((2, 0)\), you first calculate the slope \(m\) using the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-3)}{2 - 4} = \frac{3}{-2} = -\frac{3}{2} \] Using the point-slope form of the equation of a line \(y - y_1 = m(x - x_1)\) with point \((4, -3)\), we have: \[ y + 3 = -\frac{3}{2}(x - 4) \] Rearranging gives: \[ y = -\frac{3}{2}x + 6 - 3 \] So the equation of the line is: \[ y = -\frac{3}{2}x + 3 \] --- Ever wonder why studying points and lines is so essential? Well, geometry and linear equations are the building blocks of higher mathematics and play a crucial role in fields like engineering, computer graphics, and even economics! Understanding how to find the equation of a line paves the way for mastering concepts like calculus and data analysis. As you practice finding equations, be sure to double-check your calculations. A common mistake is miscalculating the slope or flipping the coordinates when applying the formula. Remember, order matters! Once you get the hang of it, solving these equations can be as satisfying as completing a puzzle. Happy calculating!