Find a linear inequality with the following solution set. Each grid line represents one unit. Answer in "standard form" ax + by + c > 0 or ax + by + c => 0 where a,b and c are integers with no common factor.
+23246 The graph appears to pass through the points (x1, y1) = (1, -2) and (x2, y2) = (3, 1).
To find the slope: m = [ y2 - y1 ] / [ x2 - x1 ] ---> y = [ 1 - -2 ] / [ 3 - 1 ] = [ 3 ] / [ 2 ] = 3/2.
Using the point-slope equation for a line: y - y1 = m(x - x1)
If the area above the line is shaded, use '>';
if the area below the line is shaded, use '<';
if the line is solid, add an equal sign;
if the line is dashed, do not add an equal sign;
so: y - -2 > (3/2)(x - 1)
y + 2 > (3/2)(x - 1)
Multiplying both sides by 2: 2y + 4 > 3(x - 1)
Using the distributive property: 2y + 4 > 3x - 3
Rearranging: -3x + 2y + 7 > 0
or: 3x - 2y - 7 < 0
