t p = through point
s = slope
[tex]y - y(t \: p) = (s) \times ( \: x - x(t \: p) \: ) \\ [/tex]
[tex]y - ( - 7) = \frac{5}{2} \times (x - 4) \\ [/tex]
[tex]y + 7 = \frac{5}{2} \times (x - 4) \\ [/tex]
[tex]y + 7 = \frac{5}{2}x - \frac{5 \times 4}{2} \\ [/tex]
[tex]y +7 = \frac{5}{2}x - \frac{20}{2} \\ [/tex]
Subtract both sides -7
[tex]y = \frac{5}{2}x - 10 - 7 \\ [/tex]
[tex]y = \frac{5}{2}x - 17 \\ [/tex]
And we're done....
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