Determine the equation of the line given by the graph. a) y = 5/7 x − 2/3 b) y = 5/7 x − 3/2 c) y = 7/5 x − 2/3 d) y = 7/5 x − 3/2

Hello!

I was going to try to use the slope formula, and solve for the y-intercept, but the given graph is hard to distinguish accurate ordered pairs. So, we will find the equation with the graph instead.

Looking at the graph, we can see that the y-intercept is negative. Also, we can also determine that each square represents one unit. So, the y-intercept has to be -3/2 or -1.5. That removes the choices A and C because the y-intercept is in between the values of -1 and -2.

Secondly, the graph has a positive slope. Why? When the x-values increase, the y-values increase. Also, when the x-values decrease, the y-values also decrease. This tells us that the graph has a positive slope (this doesn't remove any choices, but it helps to distinguish which graph has a positive or negative slope).

Finally, we know that if the slope is greater than one, then it is steeper (m > 1). But, if it's less than one, then it becomes less steep (0 < m < 1). Looking at the graph, the graph looks relatively steep (graphing the equations y = 5/7 x - 3/2 and y = 7/5x - 3/2 can help you see the differences between them).

Therefore, the equation of the line given by the graph is choice D, y = 7/5 x − 3/2.

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