Question 2: A straight line passes through \( (-4,6) \) and has a gradient of 3 . The equation of the line is:

To find the equation of the line, you can use the point-slope form \(y - y_1 = m(x - x_1)\), where \(m\) is the gradient and \((x_1, y_1)\) is a point on the line. Here, you have the point \((-4, 6)\) and the gradient \(3\). Plugging these into the formula gives you: \[ y - 6 = 3(x + 4). \] On simplifying, the equation becomes \(y = 3x + 18\). Now, let's make this even more fun! Picture yourself on a line that stretches infinitely in both directions, with a gradient of 3, meaning for every step you take to the right, you bounce up 3 steps! So imagine climbing a staircase that is both speedy and steady – that's how your line is moving through the space! If you are curious about the geometrical significance of gradients, they help us understand how steep a line is. A greater gradient means a steeper hill. In real-world applications, such as construction, understanding this steepness can guide the design of ramps or roads, ensuring that they're not too steep for safety or accessibility. So remember, whether it's hiking or building, gradients stealthily guide our way!