Question

What is the gradient of the blue line?

Answer 1

The blue line is the tangent line that passes through the point (0.75, 0.25). The point on the tangent line is (3, 4). The gradient of the curve is approximately 0.6.

Answer 2

gradient =
`(1)/(4)`

Explanation:

calculate the gradient m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (4, 2) and (x₂, y₂ ) = (8, 3) ← 2 points on the line

m =
`(3-2)/(8-4)` =
`(1)/(4)`