Final answer:
The gradient or slope of the line joining points M(4, 3) and N(9, 7) is calculated using the slope formula Δy / Δx, resulting in a slope of 4/5.
Step-by-step explanation:
The question asks to find the gradient, or slope, of the line joining two points M(4, 3) and N(9, 7).
The formula for the slope (m) is given by the difference in y-values divided by the difference in x-values, which can be expressed as Δy / Δx or (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) are the coordinates of the first point and (x₂, y₂) are the coordinates of the second point.
Using the coordinates (4,3) for M and (9,7) for N, we can calculate the slope as follows:
m = (7 - 3) / (9 - 4) = 4 / 5
Therefore, the slope of the line joining points M and N is 4/5.