Final answer:
The given linear equation, y-3+2/3(x-1), is written in point-slope form.
To convert it into slope-intercept form, we need to simplify the equation and isolate y.
Step-by-step explanation:
The given linear equation, y-3+2/3(x-1), is written in point-slope form.
To convert it into slope-intercept form, we need to simplify the equation and isolate y.
First, distribute 2/3 to x and -1: y - 3 + (2/3)x - 2/3 = y + (2/3)x - 9/3 + 2/3.
This simplifies to: y + (2/3)x - 1/3 = y + (2/3)x - 7/3.
Finally, let's isolate y by subtracting (2/3)x from both sides: y - (2/3)x - 1/3 = y - (2/3)x - 7/3 - (2/3)x.
Combining like terms yields: y - (2/3)x - 1/3 = y - (4/3)x - 7/3.
Therefore, the given linear equation is written in slope-intercept form as y = -(4/3)x - 6/3.