Question

Which graph represents ​y>1−3x?

Responses

a A graph with y axis ranging from negative 4 to 2 and x axis ranging from negative 1 to 4. A dotted line with arrows at both ends passing through the y axis at one and the x axis at point 3. The graph is shaded above the line.
Image with alt text: A graph with y axis ranging from negative 4 to 2 and x axis ranging from negative 1 to 4. A dotted line with arrows at both ends passing through the y axis at one and the x axis at point 3. The graph is shaded above the line.

b Number graph with x axis ranging from negative one to five, and y axis ranging from negative four to two. A dotted line with arrows at both ends passing through the y axis at one and the x axis at point three. The graph is shaded below the line.
Image with alt text: Number graph with x axis ranging from negative one to five, and y axis ranging from negative four to two. A dotted line with arrows at both ends passing through the y axis at one and the x axis at point three. The graph is shaded below the line.

c Number graph x axis ranging from negative one to five, and y axis ranging from negative four to two. A solid line with arrows at both ends passing through the y axis at one and the x axis at point 3. The graph is shaded below the line.
Image with alt text: Number graph x axis ranging from negative one to five, and y axis ranging from negative four to two. A solid line with arrows at both ends passing through the y axis at one and the x axis at point 3. The graph is shaded below the line.

d Number graph with y axis ranging from negative 4 to 2, and x axis ranging from negative 2 to 6. A solid line with arrows at both ends passing through the y axis at one and the x axis at point three. The graph is shaded above the line.
Image with alt text: Number graph with y axis ranging from negative 4 to 2, and x axis ranging from negative 2 to 6. A solid line with arrows at both ends passing through the y axis at one and the x axis at point three. The graph is shaded above the line.

Answer 1

Answer: a.

Reason: y > 1 − 3x is a strict inequality so the boundary is dashed (not solid). The solution is the region where y is greater than the line, i.e. above it (e.g. (0,2) gives 2 > 1). Option (a) shows a dotted line and shading above.