Answer:
[tex]y\leq \dfrac12x+3[/tex]
Step-by-step explanation:
Choose 2 points on the line: (-6, 0) and (0, 3)
- Let [tex]\sf (x_1,y_1)=(-6,0)[/tex]
- Let [tex]\sf (x_2,y_2)=(0,3)[/tex]
[tex]\sf slope=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-3}{-6-0}=\dfrac12[/tex]
point-slope form of linear equation: [tex]\sf y-y_1=m(x-x_1)[/tex]
[tex]\implies \sf y-0=\dfrac12(x-(-6))[/tex]
[tex]\implies \sf y=\dfrac12x+3[/tex]
Solid line : ≤ or ≥
Dashed line: < or >
Therefore as the line is solid, and the shading is below the line,
[tex]\implies \sf y\leq \dfrac12x+3[/tex]
