Question

On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, negative 1). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?

y > 2x + 3
y < 2x + 3
y > −2x + 3
y < −2x + 3

Answer 1

The line has slope m = (−1−3)/(2−0) = −2 and y-intercept 3, so the boundary is y = −2x + 3. It's dashed (strict) and the shaded region is left of the line; test point (−1,3) gives 3 < −2(−1)+3 = 5, so the inequality is
y < −2x + 3.