Answer:
To identify the graph of the given inequality 3y + 5x < 15, we can start by graphing the corresponding equation 3y + 5x = 15.
To graph the equation, we can rearrange it into slope-intercept form:
3y = -5x + 15
y = (-5/3)x + 5
Now, we can plot the graph of the equation y = (-5/3)x + 5. This line has a slope of -5/3 and a y-intercept of 5.
Next, we need to determine which side of the line represents the solution to the inequality 3y + 5x < 15. To do this, we can choose a test point not on the line, such as (0,0), and substitute its coordinates into the inequality:
3(0) + 5(0) < 15
0 < 15
Since the inequality is true when (0,0) is substituted, the solution to the inequality lies on the same side of the line as the point (0,0).
Therefore, the graph of the inequality 3y + 5x < 15 is the region below the line y = (-5/3)x + 5.
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