Answer:
y = - x + 6
Step-by-step explanation:
as y is the y coordinate of the final point , y1 is the y coordinate of the initial point, m is the slope or gradient of the line, x is the x coordinate of the final point, and x1 is the x coordinate of the initial point.
given (-1,7) and (2,4). 7 = y1, 4 = y, -1 = x1, 2 = x.
when substituted into the equation the unknown variable is the slope which we are solving for.
y-y1=m(x-x1) ; y = 4, y1 = 7, x = 2, x1 = -1
(given)
4-7 = m(2--1)
(substitution property of equality)
-3 = m(2--1)
(subtraction property of equality)
-3 = m(3)
(subtraction property of equality)
-3 = 3m
(multiplication property)
-1 = m.
(division property of equality)
m = -1
(symmetric property of equality)
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once m is solved you just need the initial values to solve for the actual equation.
y - y1 = m (x - x1) ; y1 = 7, m = -1, x1 = -1
(given)
y - 7 = -1 (x - -1)
(substitution property of equality)
y - 7 = -1 (x + 1)
(subtraction property if equality)
y - 7 = -x - 1
(distributive property of equality)
y = -x - 1 + 7
(addition property of equality)
y = -x + 6
(addition property of equality)