Given the points on the graph, (-3,0) and (0,5), we can solve for the slope using the formula:
m = (y2 - y1)/(x2 - x1) = (5-(-3)) / (0- (-3)) = 5/3
So the slope is 5/3 (you can verify on the graph, using the rise/run concept).
The y-intercept is the value of y when x = 0. If you look at the two coordinates that I used for solving the slope, the coordinate ( 0, 5) will give you the y-intercept of 5, since its ordered pair of x value = 0.
So, y-intercept = 5.
We now have the necessary variables needed for your linear equation:
y = 5/3x + 5.
It has a positive slope, thus the line sloping upward.
Hope this helps you :)