STEP-BY-STEP EXPLANATION:
Given information
2x + 3y < 15
To graph the above inequality, we need to find the x-intercept and the y-intercept
To find the x-intercept and y-intercept, we need to express the inequality in terms of an equation. Therefore, we have the below equation
2x + 3y = 15
To find x-intercept, isolate y by making it zero
hence, y = 0
[tex]\begin{gathered} 2x\text{ + 3(0) = 15} \\ 2x\text{ + 0 = 15} \\ 2x\text{ = 15} \\ \text{Divide both sides by 2} \\ \frac{\cancel{2}x}{\cancel{2}}\text{ = }\frac{15}{2} \\ x\text{ = }\frac{15}{2} \end{gathered}[/tex]The x-intercept is (15/2, 0)
To find y-intercept, make x = 0
[tex]\begin{gathered} 2(0)\text{ + 3y = 15} \\ 0\text{ + 3y = 15} \\ 3y\text{ = 15} \\ \text{Divide both sides by 3} \\ \frac{\cancel{3}y}{\cancel{3}}\text{ = }\frac{\cancel{15}\text{ 5}}{\cancel{3}} \\ y\text{ = 3} \end{gathered}[/tex]The y-intercept is (0, 3)
The next step is to plot the calculated coordinate points
(15/2, 0) and (0, 3)
