Answer:
Second graph
Explanation:
All the graphs have both lines intersecting at (0, -2)
In a general slope-intercept form of the line equation, we have
y = mx + b
where m is the slope, b the y-intercept
In both equations provided, the y-intercept is the same, -2
If the slope is negative, the line will go from top left to bottom right
If the slope is positive, the line will go from bottom left to top right
In the first equation, y = -1/2x - 2, the slope is negative so this line goes diagonally down from left to right
and
y = 4x - 2 has positive slope so it goes diagonally up from left to right
Looking at the first graph we see both lines have negative slope, so reject this one
The third graph has both lines going diagonally up from left to right so reject this one too
That leaves graphs 2 and 4
Let's find a point that lies on one of the graphs. Choose the second one. y = 4x - 2
Let's choose x = 1
At x = 1, y = 4x - 2 becomes 4(1) - 2 = 4 - 2 = 2
Therefore point (1, 2) should lie on the graph sloping upward. One such graph is graph 2
The 4th graph does not have (1, 2) anywhere on the line with positive slope
So the correct graph is graph 2