Answer:
We can represent this situation using an inequality in standard form, where x represents the number of cookies that Sarah sells and y represents the number of brownies that she sells. The equation would be as follows:
2x + 3y >= 500
This inequality states that the total amount of money that Sarah makes from selling cookies and brownies must be greater than or equal to $500.
To rearrange this equation into slope-intercept form, we can isolate the y term on one side of the equation. We can do this by subtracting 2x from both sides of the equation, which gives us:
3y >= 500 - 2x
We can then divide both sides of the equation by 3 to obtain:
y >= (500 - 2x) / 3
This is the slope-intercept form of the equation, where the slope is -2/3 and the y-intercept is 500/3.
To sketch a graph of this equation, we can plot the y-intercept on the y-axis and use the slope to find a second point on the line. The y-intercept is at the point (0, 500/3), and the slope tells us that for every unit increase in x, y decreases by 2/3 units. Therefore, if we increase x by 3, y will decrease by 2. This means that the second point on the line is at (3, 500/3 - 2).
We can then connect these two points with a straight line to form the graph of the inequality. This line represents all of the possible combinations of cookies and brownies that Sarah can sell in order to make at least $500. Any point on or above the line represents a combination of cookies and brownies that meets this requirement, while points below the line do not.