1. **State the problem:** Find the gradient and the coordinates of the x and y intercepts of the line given by the equation $$2y - 3x = 1$$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y = mx + c$$ where $m$ is the gradient and $c$ is the y-intercept. Starting with $$2y - 3x = 1$$, add $3x$ to both sides: $$2y = 3x + 1$$ Divide both sides by 2: $$y = \frac{3}{2}x + \frac{1}{2}$$ 3. **Identify the gradient:** From the equation $$y = \frac{3}{2}x + \frac{1}{2}$$, the gradient $m = \frac{3}{2}$. 4. **Find the y-intercept:** The y-intercept occurs when $x=0$. Substitute $x=0$: $$y = \frac{3}{2} \times 0 + \frac{1}{2} = \frac{1}{2}$$ So, the y-intercept is at $$\left(0, \frac{1}{2}\right)$$. 5. **Find the x-intercept:** The x-intercept occurs when $y=0$. Set $y=0$ in the original equation: $$2(0) - 3x = 1 \implies -3x = 1 \implies x = -\frac{1}{3}$$ So, the x-intercept is at $$\left(-\frac{1}{3}, 0\right)$$. **Final answers:** - Gradient: $$\frac{3}{2}$$ - x-intercept: $$\left(-\frac{1}{3}, 0\right)$$ - y-intercept: $$\left(0, \frac{1}{2}\right)$$