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write the slope intercept form of the equation with the given characteristic passes through (2,-2) & (4,1)

1 Answer

3 votes

Answer:


y = (3)/(2)x - 5

Explanation:

General format for the slope-intercept form of an equation:


y = mx + c

where:

m = slope

c = y-intercept


(x_(1) , y_(1)) =
(2, -2)


(x_(2) ,y_(2)) =
(4, 1)

m =
(y_(2) -y_(1))/(x_(2) - x_(1))

=
(1- (-2))/(4-2)

=
(1+2)/(2)

m =
(3)/(2)

Substituting this value of m into our equation:


y = (3)/(2)x + c

Substituting the coordinates of any of the two points into the above equation to solve for c:

1 =
(3)/(2)(4) + c

1 =
(12)/(2) + c

1 = 6 + c

Isolate c and make it the subject of the equation:

c =
1 -6

c =
-5

∴The slope-intercept form of the equation after substituting the calculated values of m and c:


y = (3)/(2)x + (-5)


y = (3)/(2)x - 5

User Jolestar
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