Final answer:
To convert X - 3y = 9 to slope-intercept form, subtract X from both sides, divide by -3, and simplify to get y = (1/3)X - 3 with a slope of 1/3 and a y-intercept of -3.
Step-by-step explanation:
To convert the equation X - 3y = 9 into slope-intercept form, which is y = mx + b where m is the slope and b is the y-intercept, follow these steps:
- Begin with the original equation: X - 3y = 9.
- Move the term with X to the other side by subtracting X from both sides of the equation: -3y = -X + 9.
- Divide each term by the coefficient of y, which is -3: y = -(-X + 9)/-3.
- Simplify the division to find the slope-intercept form: y = (1/3)X - 3.
The equation is now in slope-intercept form, with the slope m being 1/3 and the y-intercept b being -3. This tells you for each increase of 1 on the horizontal axis (X), there is an increase of 1/3 on the vertical axis (y), and the line will cross the y-axis at -3.