Answer: To find the equation of a line that is parallel to the graph of y = -2/3x + 12 and passes through the point (6, -11), we can use the fact that parallel lines have the same slope.
1. Identify the slope of the given line. The equation y = -2/3x + 12 is in slope-intercept form (y = mx + b), where the coefficient of x (m) represents the slope. In this case, the slope is -2/3.
2. Use the slope-intercept form of a linear equation (y = mx + b) and the given point (6, -11) to find the equation of the parallel line. Since the slope is the same, we can write the equation as:
y = -2/3x + b
3. Substitute the coordinates (x, y) of the given point (6, -11) into the equation to solve for the y-intercept (b):
-11 = -2/3(6) + b
4. Simplify the equation and solve for b:
-11 = -4 + b
b = -11 + 4
b = -7
5. Substitute the value of b (-7) into the equation:
y = -2/3x - 7
Therefore, the equation in slope-intercept form of the line that passes through (6, -11) and is parallel to the graph of y = -2/3x + 12 is y = -2/3x - 7.
Explanation: