Question 4: A straight line that passes through \( (0,5) \) and \( (4,17) \). The equation of the line is

To find the equation of the line passing through \( (0,5) \) and \( (4,17) \), we start by calculating the slope \( m \) using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Here, \( (x_1, y_1) = (0, 5) \) and \( (x_2, y_2) = (4, 17) \). Thus, \( m = \frac{17 - 5}{4 - 0} = \frac{12}{4} = 3 \). With the slope known, we can use the point-slope form \( y - y_1 = m(x - x_1) \) and plug in \( (0, 5) \): \[ y - 5 = 3(x - 0) \] This simplifies to: \[ y = 3x + 5 \] So the equation of the line is \( y = 3x + 5 \). --- The world of line equations is not just for math enthusiasts; it’s a powerful tool in various fields! In architecture, for instance, understanding linear relationships can help design structures that are not only aesthetically pleasing but also structurally sound. How about putting those equations to use in planning your dream treehouse? Ever tried graphing a line and accidentally mixed up your coordinates? It happens more often than you'd think! A common pitfall is not properly calculating the slope or misplacing the y-intercept. Always double-check your points before diving into slope calculations and remember—coordinate systems have your back, so don’t hesitate to use graph paper or digital tools to visualize!