Question

Which is the ordered pair for the point on the x-axis
that is on the line parallel to the given line and through
the given point (-6, 10)?
(6,0)
(0,-3) (-5,0) (0,-5)

Answer 1

The ordered pair for the point on the x-axis  that is on the line parallel to the given line and through  the given point (-6, 10) is:

$\boxed{(6,0)}$

Explanation:

The complete question includes a graph. I have found it on the internet and has been attached below. So:

OUR GOAL:

To find an ordered pair for the point on the x-axis  that is on the line parallel to the given line and through  the given point (-6, 10)

With two points we can get the slope of a line, so for the given linewe have the following slope (m):

$P_{1}(-8,6) \\ \\ P_{2}(4,-4) \\ \\ \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ m=\frac{-4-6}{4-(-8)} \\ \\ m=-\frac{10}{12}=-\frac{5}{6}$

Since the line we are looking for is parallel to the given line, then the slope of our unknown line (let's call it $m_{x}$) equals the slope of the given line. In other words:

$m_{x}=m=-\frac{5}{6}$

The point slope form of the equation of a line is:

$y-y_{0}=m(x-x_{0}) \\ \\ Where: \\ \\ P_{0}(x_{0},y_{0}) \ is \ a \ point \ on \ the \ line \\ \\ Here: \\ \\ P_{0}(-6,10) \\ \\ \\ Accordingly: \\ \\ y-10=-\frac{5}{6}(x-(-6)) \\ \\ y-10=-\frac{5}{6}(x+6)$

Finally, to find the ordered pair on the x-axis let's set $y=0$ then:

$y-10=-\frac{5}{6}(x+6) \\ \\ 0-10=-\frac{5}{6}(x+6) \\ \\ Isolating \ x: \\ \\ -\frac{5}{6}x-5=-10 \\ \\ \\ Add \ 5 \ to \ both \ sides: \\ \\ -\frac{5}{6}x-5+5=-10+5 \\ \\ -\frac{5}{6}x=-5 \\ \\ \\ Multiply \ by \ -\frac{6}{5} \ both \ sides: \\ \\ (-\frac{6}{5})(-\frac{5}{6}x)=(-5)(-\frac{6}{5}) \\ \\ \boxed{x=6}$

Finally, the ordered pair is given by:

$\boxed{(x,y) \rightarrow (6,0)}$

Learn more:

Equation of a line: https://brainly.com/question/12169569

#LearnWithBrainly

Answer 2

Answer:

a

Step-by-step explanation: