Question

Write the equation of the line in standard form
64. contains (-8, 4)
and the midpoint of the
segment connecting
(-10, 5) and (-5, 0). Show your work.

Answer 1

Answer:

$\bold{3x+y+20=0}$

Step-by-step explanation:

Mid point of (-10, 5) and (-5, 0).

Other point (-8, 4).

To find:

Equation of line in standard form that connect the mid point and other point.

Solution:

Mid point formula is given as:

$x = \dfrac{x_1+x_2}{2}\\y = \dfrac{y_1+y_2}{2}$

$x = \dfrac{-10+-5}{2} = -7.5\\y = \dfrac{5+0}{2} = 2.5$

Now, the two points are: (-7.5, 2.5) and (-8, 4)

Slope intercept form of line is given as:

$y = mx+c$

$m=\dfrac{4-2.5}{-8-(-7.5)} = -3$

So, the equation of line is:

$\Rightarrow y =-3x+c$

Putting (-8, 4) to find c:

$4=-3\times -8+c\\\Rightarrow c = -20$

Equation of line:

$\Rightarrow y =-3x-20$

In standard form:

$\bold{3x+y+20=0}$