Hi there!
[tex]\large\boxed{\left \{ {{y\geq -x + 3} \atop {y > 2x - 3}} \right.}[/tex]
We can begin by looking at the solid-line pictured in the graph.
Using the slope-formula, we can derive the slope from this line:
[tex]\text{Slope } = \frac{ y_2 - y_1 } { x_2 - x_1 }[/tex]
Plug in points from the line:
[tex]m = \frac{0- 3 } { 3 - 0} = -1[/tex]
We can also see that the graph has a y-intercept, or "b" value of 3. The line is a solid line including values above it, which means we must use a "greater than or equal to" symbol. Therefore, the final equation is:
y ≥ -x + 3
The second line is dashed and also has values shaded above its graph. We can use this later to make an equation, but let's solve for the slope for now. Use the same equation as above:
[tex]m = \frac{1-(-3)}{2-0} = 4/2 = 2[/tex]
The graph has a y-intercept at y = -3, so this is the "b" value in its slope-intercept formula.
Use a "greater than" sign (Not equal to... the line is dashed) to write the equation:
y > 2x - 3
