To determine the gradient (slope) and the y-intercept of the line given by the equation $2x + 3y = 6$, we need to rewrite the equation in the slope-intercept form, $y = mx + c$, where $m$ is the gradient and $c$ is the y-intercept.

Steps:

1. Start with the equation: $2x + 3y = 6$

2. Solve for $y$ to get the equation into the slope-intercept form: $3y = -2x + 6$ $y = -\frac{2}{3}x + 2$

Results:

• Gradient (slope) $m$: $-\frac{2}{3}$
• Y-intercept $c$: $2$

So, the gradient of the line is $-\frac{2}{3}$, and the y-intercept is $2$.

Would you like more details or have any questions?

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Here are 5 related questions for further practice:

1. Determine the gradient and y-intercept of the line $4x - 5y = 10$.
2. What is the equation of a line parallel to $y = -\frac{2}{3}x + 4$?
3. Find the equation of a line that passes through the point $(1, 3)$ with a slope of $-\frac{2}{3}$.
4. Calculate the x-intercept of the line $2x + 3y = 6$.
5. Convert the equation $6x - 2y = 12$ into slope-intercept form and find its gradient.

Tip: Always convert a linear equation into the slope-intercept form to easily identify the gradient and y-intercept.