Part 1 of 2 Write the point-slope form of the line satisfying the given conditions. Then use the point-slope form of the equation to writ the slope-intercept form of the equation. Passing through \( (4,8) \) and \( (7,14) \) Iype the point-slope torm ot the equation ot the line. (Simplify your answer. Use integers or fractions for any number in the equation.)

To find the point-slope form of the line passing through the points (4,8) and (7,14), we first need to calculate the slope \( m \). The slope formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{14 - 8}{7 - 4} = \frac{6}{3} = 2 \] Now, using the point-slope form formula \( y - y_1 = m(x - x_1) \) with point (4,8): \[ y - 8 = 2(x - 4) \] Next, we simplify this to get the slope-intercept form \( y = mx + b \): \[ y - 8 = 2x - 8 \\ y = 2x \] So the point-slope form of the equation is \( y - 8 = 2(x - 4) \) and the slope-intercept form is \( y = 2x \). --- Did you know that the concept of linear equations and slope dates back to ancient civilizations? The earliest recorded uses were by the Babylonians, who had methods for solving linear equations around 2000 BC! Imagine calculating parallel lines on a clay tablet! If you're navigating a real-world problem, remember the incredible utility of slope in fields like engineering, economics, and even sports analytics! Whether you’re measuring the rise of a roof or analyzing the trajectory of a basketball shot, understanding how to find slopes helps you visualize and manipulate real-life scenarios effectively!