Answer: " y = (2/3)x − (13/3) " .
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Note: "point-slope" form; or "slope-intercept form" is:
"y = mx + b" ;
in which "y" is on the left-hand side of the equation, with NO coefficient (except for the "implied coefficient of "1");
m = the slope; and is the coefficient of "x" ;
b = the y-intercept; or the value of "x" at the point which "y = 0" .
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We are given the following point on the line: (5, -1).
We are given the slope, " m = 2/3 " .
Note the formula:
y − y₁ = m(x − x₁) ; Given "x₁ = 5" ; "y₁ = -1" ; "m = 2/3" ;
Plug in these known values into the formula:
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y − (-1) = (2/3)*(x − 5) ;
to get:
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y + 1 = (2/3)x − (2/3)*(5) ;
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Note: 5* (2/3) = 5/1 * 2/3 = (5*2)/(1*3) = 10/3
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y + 1 = (2/3)x − 10/3 ;
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Subtract "1" from EACH side of the equation:
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y + 1 − 1 = (2/3)x − (10/3) − (1) ; {Note: "3/3 = 1"}.
Rewrite as:
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y + 1 − 1 = (2/3)x − (10/3) − (3/3) ;
to get:
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y = (2/3)x − (13/3) .
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