Answer: y > (5/2)*x - 3
Step-by-step explanation:
Ok, the thins we should notice.
The line is shaded, so the values of the line are not solutions of the inequality, then we should use < or >.
The shaded part is above the line, so we have:
y > a*x + b.
A linear relationship can be written as:
f(x) = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Now, we know that our line passes through the points (0, -3) and (2, 2)
Then the slope is:
a = (2 -(-3))/(2 - 0) = 5/2.
f(x) = (5/2)*x + b.
To find the value of b, we can replace the values of one of the points in the equation, let's use the point (0, -3)
f(0) = -3 = (5/2)*0 + b
-3 = b
Then the line is:
f(x) = (5/2)*x - 3
Then the inequality is:
y > (5/2)*x - 3
