Answer:
(c) 6x − y < −3
Explanation:
You want to know which inequality has shading above the dashed line through (0, 3) and (1, 9).
Boundary line
The first given point is the y-intercept of the boundary line: 3. The two points together can be used to find the slope:
m = (y2 -y1)/(x2 -x1)
m = (9 -3)/(1 -0) = 6
This means the slope-intercept equation of the line is ...
y = mx +b
y = 6x +3
Rearranging to standard form, this is ...
6x -y = -3
The fact that the boundary line is dashed means the inequality symbol will not include the "equal to" case. It will be one of < or >.
Shading
The shading above the line with positive slope is the same as shading to the left of that line. That is, x-values in the solution set will be less than x-values on the line. The inequality will be ...
6x -y < -3
__
Additional comment
You can determine line type and shading by looking at the inequality symbol and a variable with a positive coefficient. In the above inequality, x has a positive coefficient, so that is the one we considered when looking at shading. X-values less than those on the line means the relation shown in the inequality will be ...
x <
Shading above the line would look like ...
y >
In our equation for the boundary line, the coefficient of y is negative. Multiplying this inequality by -1 would give ...
-y <
Hence the inequality 3x -y < -3 is consistent with a dashed line having shading above and to the left.
If the symbols are < or >, the line is dashed. If they are ≤ or ≥, the line is solid.