Which point is located on the line represented by the equation y-5=2/3 (x+9)?
To determine the point located on the line represented by the equation y - 5 = (2/3)(x + 9), we need to solve for the values of x and y.
First, distribute the 2/3 to the terms inside the parentheses on the right side of the equation:
y - 5 = (2/3)x + (2/3)(9)
Simplify further:
y - 5 = (2/3)x + 6
Next, add 5 to both sides of the equation to isolate the y-term on the left side:
y = (2/3)x + 11
Now, we have the equation in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. Here, the slope is 2/3, and the y-intercept is 11.
Since we are looking for a point on the line, we need specific x and y values. Let's choose an arbitrary value for x and use the equation to find the corresponding y value.
Let's say x = 0. Plugging this into the equation y = (2/3)x + 11 gives:
y = (2/3)(0) + 11
y = 0 + 11
y = 11
Thus, the point located on the line represented by the equation y - 5 = (2/3)(x + 9) is (0, 11).