Final answer:
The given equation 4x-3y=9 can be converted into slope-intercept form by isolating y and simplifying the equation, resulting in y=(4/3)x-3.
Step-by-step explanation:
To put the equation 4x-3y=9 into slope-intercept form, we need to solve for y. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. Here's how we can transform the equation:
Subtract 4x from both sides of the equation to isolate terms with y on one side: 4x - 4x - 3y = 9 - 4x which simplifies to -3y = -4x + 9.
Divide each term by -3 to solve for y: y = (4/3)x - 3.
The correct slope-intercept form of the line is y = (4/3)x - 3, which means that option a) Y=4/3x-3 is the correct answer.