which is the graph of $y - 3 = -\\frac{2}{3}(x + 6)$?
which is the graph of $y - 3 = -\\frac{2}{3}(x + 6)$?
Answer
Explanation:
Step1: Identify the point - slope form
The equation (y - y_1=m(x - x_1)) is the point - slope form of a line, where ((x_1,y_1)) is a point on the line and (m) is the slope. For the equation (y - 3=-\frac{2}{3}(x + 6)), we have (m =-\frac{2}{3}), (x_1=-6), and (y_1 = 3).
Step2: Check the point ((-6,3)) on the graph
We look for the graph that passes through the point ((-6,3)).
Step3: Verify the slope
The slope (m =-\frac{2}{3}=\frac{\Delta y}{\Delta x}). If (x) increases by (3), (y) decreases by (2).
Answer:
The graph that passes through the point ((-6,3)) with a slope of (-\frac{2}{3}) is the correct one. (Since we don't have the actual labels for each graph in text - based format, but by using the point - slope form properties (point ((-6,3)) and slope (-\frac{2}{3}) to check each of the given graphs in the original problem's image, we can identify the right graph).