Question

PLZ HELP ;(((

Answer 1

Answer:

The value of k is -4 and the equation of the line is $y =-\frac{1}{2}\cdot x +10$.

Step-by-step 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:

$m = \frac{y-y_{o}}{x-x_{o}}$ (2)

Where $x_{o}$ and $y_{o}$ are the coordinates of the reference point.

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

$y = \frac{y-y_{o}}{x-x_{o}}\cdot x + b$

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

$x\cdot y -y\cdot x_{o} = x\cdot y -x\cdot y_{o}+b\cdot x -b\cdot x_{o}$

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

$(b-y)\cdot x_{o} +x\cdot y_{o} = b\cdot x$ (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:

$m = \frac{9-7}{2-6}$

$m = -\frac{1}{2}$

The equation of the line is $y =-\frac{1}{2}\cdot x +10$.