What is the gradient of the line that passes through the points
and ?
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To find the gradient (or slope) of the line that passes through the points and , you can use the formula:

Substituting in your points, as and as :

So, the gradient of the line is .

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!