in the graph for the solution set of the inequality 4x - 3y > 6, identify the coordinate that is a solution.
To identify the coordinates that are solutions to the inequality 4x - 3y > 6, we need to find the points that lie on or above the corresponding graph.
First, we can rewrite the inequality in slope-intercept form. Subtracting 4x from both sides, we have -3y > -4x + 6. Dividing both sides by -3 but flipping the inequality sign, we get y < (4/3)x - 2.
This inequality represents a line with a slope of 4/3 and a y-intercept of -2. To graph it, we can plot the y-intercept (-2) on the y-axis and use the slope to determine the next point. From the y-intercept, we can go up 4 units and then go right 3 units to locate another point.
Connecting these two points, we can draw a dashed line since it does not include the points on the line itself. This dashed line represents the graph of the inequality y < (4/3)x - 2.
Now, any points below this line are solutions to the inequality. For example, the point (2, 0) is below the line and is therefore a solution. The coordinate (2, 0) represents x = 2 and y = 0.
In summary, the coordinate (2, 0) is a solution to the inequality 4x - 3y > 6.