Question 5:
A straight line passes through 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 . Plugging in the point and the gradient , the equation becomes . Simplifying this gives , which simplifies to .

Now you have the equation of the line as . 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!