For this type of question when we're trying to determine the equation of a line, we first need to find the slope of the line and insert it along with a (x,y) coordinate into the Point-Slope Formula.
The point slope formula is, y-y₁=m(x-x₁). We are given a coordinate point and the slope so we plug in our given values. We can label our given coordinate point ( 1, -2 ) x1 which is 1 and y1 which is -2. Furthermore, we plug x1, y1, and m (our given slope) which is -2/3 into our Point-Slope Formula.
We then get:
- y - (-2)=-2/3(x-1)
Simplifying we get:
- y + 2 = - 2/3x + 2/3
We then subtract the 2 from the left side over to the right to form a complete equation and have it in the form of y = mx + b (Slope-Intercept Form):
- y= -2/3x - 4/3
You can then multiply the entire equation by 3 to get rid of the 3's in the denominator:
- 3y = -2x - 4
Lastly we can move the 2x over to have it in standard form, which is ( Ax + By = C):
- 3y + 2x = - 4 , where this is your final answer.
- Please let me know if there are any steps i can clarify for you.