Subjects algebra

Line Gradient Yintercept 4Cc0Ef

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1. **State the problem:** We need to find the gradient (slope) and the y-intercept of the line shown on the graph. 2. **Identify points on the line:** From the graph description, two points on the line are approximately $A=(0,20)$ and $B=(15,60)$. 3. **Formula for gradient:** The gradient $m$ of a line passing through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by: $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ 4. **Calculate the gradient:** Substitute $A$ and $B$ into the formula: $$m=\frac{60 - 20}{15 - 0}=\frac{40}{15}$$ 5. **Simplify the fraction:** $$m=\frac{\cancel{40}}{\cancel{15}}=\frac{8}{3}$$ 6. **Find the y-intercept:** The y-intercept is the value of $y$ when $x=0$. From point $A$, the y-intercept is $20$. **Final answers:** - Gradient (slope) $m=\frac{8}{3}$ - Y-intercept $=20$