Subjects algebra

Line Gradient Fcb328

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1. The problem asks us to find the gradient (slope) of the line passing through two points on the graph. 2. The gradient formula is: $$\text{Gradient} = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. From the graph, the two points are approximately $(1,1)$ and $(4,7)$. 4. Substitute these values into the formula: $$\text{Gradient} = \frac{7 - 1}{4 - 1} = \frac{6}{3}$$ 5. Simplify the fraction: $$\text{Gradient} = \frac{\cancel{6}}{\cancel{3}} = 2$$ 6. Therefore, the gradient of the line is $2$. This means for every 1 unit increase in $x$, $y$ increases by 2 units.