determine the gradient and the y-intercept of the line 2x+3y=6

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 \( 2 \).

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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.

Learn how to determine the gradient (slope) and y-intercept of the line given by the equation 2x + 3y = 6. This problem covers the conversion of a linear equation into slope-intercept form, identifying the gradient and y-intercept. Suitable for Grades 7-9.

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