Explanation:
A. When you examine the values in the table, you see the y-value is not proportional to the x-value. That is, 20/1 ≠ 26/2. However, you do notice that the y-values increase by 6 when the x-values increase by 1. <em>The ratio of these increases is the slope of the graph of the relation between y and x</em>.
Since the slope is 6, we might expect a value of 6×1 = 6 for x=1. However, the y-value for x=1 is 20, which is 14 more than what might be predicted by the slope. <em>This added extra is the y-intercept on the graph of the relation</em>.
The slope is 6 and the y-intercept is 14.
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B. The slope is (26-20)/(2-1) = 6.
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C. For x=1, the slope-intercept equation tells us ...
y = 6x +b
20 = 6·1 + b . . . . . . . . . . substitute (x, y) = (1, 20)
20 -6 = 14 = b . . . . . . . . subtract 6 to find b
