Subjects algebra

Line Gradient Y Intercept

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** We need to find the gradient (slope) and the y-intercept of the line passing through the points approximately (0, 5) and (20, 60). 2. **Formula for gradient:** The gradient $m$ of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate the gradient:** Using the points $(0, 5)$ and $(20, 60)$: $$m = \frac{60 - 5}{20 - 0} = \frac{55}{20} = 2.75$$ 4. **Find the y-intercept:** The y-intercept $b$ is the value of $y$ when $x=0$. From the point $(0, 5)$, the y-intercept is: $$b = 5$$ 5. **Equation of the line:** Using the slope-intercept form $y = mx + b$: $$y = 2.75x + 5$$ **Final answer:** - Gradient (slope) = $2.75$ - Y-intercept = $5$