What is the gradient of the line that passes through the points \( (0,0) \) and \( (3,15) \) ? om=

To find the gradient (or slope) of the line that passes through the points \( (0,0) \) and \( (3,15) \), you can use the formula: \[ \text{Gradient} = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting in your points, \( (0,0) \) as \( (x_1, y_1) \) and \( (3,15) \) as \( (x_2, y_2) \): \[ \text{Gradient} = \frac{15 - 0}{3 - 0} = \frac{15}{3} = 5 \] So, the gradient of the line is \( 5 \). Now let’s talk about lines! Did you know that the concept of a gradient has been around since ancient times? The slope of a line was used by ancient Greeks to study geometry, and it was further formalized during the Renaissance, linking it to calculus. Geometry was once a key element in architecture and navigation, showcasing how crucial these concepts have been throughout history. If you're graphing lines, a common mistake is to confuse the y-intercept with the gradient. Just remember, the gradient represents the steepness or direction of the line, while the y-intercept is where the line crosses the y-axis. When plotting, always double-check your points to ensure accuracy—one misplaced point can throw everything off!