During a snowstorm, the relationship between the depth of accumulated snow, y inches, and the elapsed time, x hours, was modeled by the equation 2x - 5y = -5. One of the following graphs in the standard (x, y) coordinate plane models the equation for positive values of x and y. Which one?
The correct answer is A.
The correct graphical model can be identified by considering the slope and the y-intercept of the graph of the equation 2x - 5y = -5. Writing this equation in slope-intercept form, we get
y = 2x/5 + 1
From this, the slope is 2/5 and the y-intercept is 1. From the y-intercept alone, we can rule out C, D, and E because the y-intercepts of those graphs are 0, 5, and 5, respectively.
The graph in B appears to pass close to the point (2, 6). Using that point and (0, 1), along with slope in terms of the change in y over the change in x, the slope of the graph in B is approximately (6 - 1)/(2 - 0) = 5/2.
However, the graph in A appears to pass close to the point (5, 3). Again, using that point and (0, 1), along with slope in terms of the change in y over the change in x, the slope of the graph in A is approximately (3 - 1)/(5 - 0) = 2/5.