Subjects algebra

Line Gradient Fbbc4D

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1. **State the problem:** We need to find the gradient (slope) of the straight line shown on the graph. 2. **Recall the formula for gradient:** The gradient $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ This formula calculates the "rise" over the "run," or how much $y$ changes for a unit change in $x$. 3. **Identify points on the line:** From the graph, the line passes through the origin $(0,0)$ and approximately the point $(6, 45)$. 4. **Calculate the gradient:** Substitute the points into the formula: $$m = \frac{45 - 0}{6 - 0} = \frac{45}{6} = 7.5$$ 5. **Interpretation:** The gradient of 7.5 means that for every 1 unit increase in $x$, $y$ increases by 7.5 units. **Final answer:** The gradient of the line is $7.5$.