Subjects algebra

Line Gradient 0F71F9

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

Use the AI math solver

1. The problem asks us to find the gradient (slope) of a straight line shown on a grid. 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 description, the line descends from left to right, so the gradient will be negative. 4. Identify two points on the line using the grid cells. Suppose the line passes through points $A(0,6)$ (top-left) and $B(8,0)$ (bottom-right). 5. Calculate the change in $y$: $$y_2 - y_1 = 0 - 6 = -6$$ 6. Calculate the change in $x$: $$x_2 - x_1 = 8 - 0 = 8$$ 7. Substitute into the gradient formula: $$\text{Gradient} = \frac{-6}{8}$$ 8. Simplify the fraction by dividing numerator and denominator by 2: $$\frac{\cancel{-6}^{\,-3}}{\cancel{8}^4} = \frac{-3}{4}$$ 9. Therefore, the gradient of the line is: $$\boxed{-\frac{3}{4}}$$