First look at the place where the line crosses the x-axis and where it crosses the y-axis. The x-intercept is at the point (5/2,0) and the y-intercept is at the point (0,-1). From these two points we can calculate the slope of the line, which should be positive since the line has an upward incline. Mathematically, the slope is defined as the change is y divided by the change in x: we can calculate each using the two points (5/2,0) and (0,-1).

slope = [0 - (-1)]/[5/2 - 0] = 1/(5/2) = 2/5 = m and the standard equation of a line is y = m*x + b. We now know that

y = (2/5)*x + b. We need to determine b. Notice from that graph that when x = 0, y = -1. Plug these two values into the previous equation and you get

-1 = (2/5)*0 + b, which means that b = -1 since (2/5)*0 = 0.

So, the relationship between x and y as shown in the line is best described mathematically as y = (5/3)*x - 1.

Whoops. 5/2 should have been 3/2. Let me redo here.

The x-intercept is at the point (3/2,0) and the y-intercept is at the point (0,-1). From these two points we can calculate the slope of the line, which should be positive since the line has an upward incline. Mathematically, the slope is defined as the change is y divided by the change in x: we can calculate each using the two points (3/2,0) and (0,-1).

slope = [0 - (-1)]/[3/2 - 0] = 1/(3/2) = 2/3 = m and the standard equation of a line is y = m*x + b. We now know that

y = (2/3)*x + b. We need to determine b. Notice from that graph that when x = 0, y = -1. Plug these two values into the previous equation and you get

-1 = (2/3)*0 + b, which means that b = -1 since (2/3)*0 = 0.

So, the relationship between x and y as shown in the line is best described mathematically as y = (2/3)*x - 1.

In terms of the options given, it would be: Option D. Sorry about that. Let me know if you find any other issues.

Apr 22nd, 2015

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