From the table, it is obvious that the y values increase by 9 every increase of 4 of the x values. So, the slope is 9/4 and the function looks like this:

$y = m x+ b = \frac{9}{4}x + b$

with the y-intercept (or bias) b still unknown. This can be determined by using one of the point from the table, like so:

$-18 = \frac{9}{4}\cdot 2+b\\\implies b = -18 -\frac{9}{2}=\frac{45}{2}\\y = \frac{9}{4}x+\frac{45}{2}$

The above function form makes it easy to read off the y-intercept, which is (0,45/2) or (0,22.5). The x-intercept is obtained by setting y = 0 and solving for x:

$y = \frac{9}{4}x+\frac{45}{2}\\0 = \frac{9}{4}x+\frac{45}{2}\\-\frac{45}{2}=\frac{9}{4}x\\x = -10$

The x-intercept is (-10,0)

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3 years ago

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