Answer:
C. y<5/3x-3
Explanation:
First, treat this problem as if you were graphing a normal slope intercept form equation, y=mx+b, where m=slope and b=the y-intercept. To find the slope of the line, find two points on the graph and count the number of units up/down over the number of units right/left. You could also use the slope formula, (y2-y1)/(x2-x1).
Once you have the slope, which, in this equation, is 5/3, find b, the y-intercept. You can find it by seeing where the line intersects with the y-axis (the vertical axis). In this case, b=(-3).
If this was a normal line, the equation would be y=5/3x-3. However, it's an inequality, and we're not quite done yet. We can eliminate answer B.
Look closely at the line. If it's dotted, the symbol is either a less-than/greater-than symbol (< or >). That means the answer can be any number up to that OR any number above that, but not that exact number. If it's a solid line, that means it's either a less-than or equal-to/greater-than or equal-to symbol, which looks like < and >. That means the answer can be that number and any number up to it OR that number and any number above it. This graph shows a dotted line, so we can eliminate answer A.
Now, one of the hardest parts, though it's really quite easy. If an equation is less-than or less-than or equal-to, the shaded region (all the possibilities) would be below the line. This is easy to tell with a horizontal line, easy enough to tell with a diagonal line, and a little difficult with a vertical line. With a vertical line, think of a number line with a single point on it. Anything to the left of the point is less than the point, so you would shade to the left of the line. If an equation is greater-than or greater-than or equal-to, the shaded region would be above the line, because it's the opposite of less-than or less-than or equal-to. Because the shaded region is below the line, the symbol to use in this equation is < because the answer is unknown but definitely below that line, but not on the line, because it's not a solid line, which means the answer is included.
The inequality of this line is y<5/3x-3, which is listed as answer C. Hope that helped! Comment if it didn't make sense.