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PLZ HELP ;(((

A line passes through the points (k + 10,-2k – 1) and (2,9) and has a y-intercept
of 10. Find the value of k and the equation of the line.
solve for all 3 equations

User Bromanko
by
8.3k points

1 Answer

12 votes

Answer:

The value of k is -4 and the equation of the line is
y =-(1)/(2)\cdot x +10.

Explanation:

The equation of the line is defined by the following formula:


y = m\cdot x + b (1)

Where:


x - Independent variable.


y - Dependent variable.


b - y-Intercept.


m - Slope.

In addition, the slope of the equation of the line (
m) can be known from two distinct points:


m = (y-y_(o))/(x-x_(o)) (2)

Where
x_(o) and
y_(o) are the coordinates of the reference point.

By applying (2) in (1), we derive the resulting expression:


y = (y-y_(o))/(x-x_(o))\cdot x + b


y\cdot (x-x_(o)) = (y-y_(o))\cdot x + b\cdot (x-x_(o))


x\cdot y -y\cdot x_(o) = x\cdot y -x\cdot y_(o)+b\cdot x -b\cdot x_(o)


(b-y)\cdot x_(o) = b\cdot x -x\cdot y_(o)


(b-y)\cdot x_(o) +x\cdot y_(o) = b\cdot x (3)

If we know that
b = 10,
x = 2,
y = 9,
x_(o) = k+10 and
y_(o) = -2\cdot k -1, then the value of
k is:


(10-9)\cdot (k+10)+2\cdot (-2\cdot k -1) = (10)\cdot (2)


k+10 -4\cdot k -2 = 20


-3\cdot k +8 = 20


-3\cdot k = 12


k = -4

The value of the slope is:


m = (9-7)/(2-6)


m = -(1)/(2)

The equation of the line is
y =-(1)/(2)\cdot x +10.

User Abhishake
by
8.6k points

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