It may be convenient here to write the equation of the line as
... ∆y(x -x0) -∆x(y -y0) = 0
where (x0, y0) is a point on the line, and (∆x, ∆y) is the difference between two points on the line.
Using the first two points, we have
... (∆x, ∆y) = (-9, 10) - (-15, 5) = (6, 5)
So, the equation of the line is
... 5(x +9) -6(y -10) = 0 . . . . . . using the point (x0, y0) = (-9, 10)
... 5x -6y = -105 . . . . . . . . . . . simplify to standard form
Now, dividing by the constant on the right, we can put this into intercept form
... x/(-21) +y/(17.5) = 1
This tells us the y-intercept is (0, 17.5) and the x-intercept is (-21, 0).
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You can work directly with the values in the table. The y-value increases by 5 from one line to another, while the x-value increases by 6. Thus, to make the y-value decrease by 5 from the first point, we need to decrease that point's x-value by 6 to -21. That is, the x-intercept is (-21, 0).
Similarly, the x-value need to increase by only 3 from the last point. That amounts to half of the usual increase of 6. Thus the y-intercept will be the last point plus have the usual y-increase of 5, or 15+2.5 = 17.5. That is, the y-intercept is (0, 17.5).
