Question 5: A straight line passes through \( (2,5) \) and has a gradient of -4 . The equation of the line is:

To find the equation of a line with a given point and gradient, you can use the point-slope form of the line equation, which is \( y - y_1 = m(x - x_1) \). Plugging in the point \( (2, 5) \) and the gradient \( m = -4 \), the equation becomes \( y - 5 = -4(x - 2) \). Simplifying this gives \( y = -4x + 8 + 5 \), which simplifies to \( y = -4x + 13 \). Now you have the equation of the line as \( y = -4x + 13 \). Happy graphing! Did you know that gradient, or slope, essentially indicates how steep a line is? A negative gradient means the line descends from left to right – like a slide down the playground! This simple concept lays the groundwork for understanding multiple mathematical scenarios, from economics to physics. Funny enough, a common mistake when dealing with line equations is mixing up the coordinates or the signs of the gradient. Double-checking your points and ensuring the slope is applied correctly can save you from those "oops" moments! Comparing your calculations visually on a graph can also help you catch any errors before they stick!