Answer:
The equation of the line that passes through the given points is:
Hence, option D is correct.
The graph of the line equation is also attached below.
Step-by-step explanation:
Given the points
Finding the slope between (-5, 10) and (5, -10)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-5,\:10\right),\:\left(x_2,\:y_2\right)=\left(5,\:-10\right)[/tex]
[tex]m=\frac{-10-10}{5-\left(-5\right)}[/tex]
[tex]m=-2[/tex]
Using the point-slope form to determine the line equation
Point slope form:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = -2 and the point (-5, 10)
[tex]y-10=-2\left(x-\left(-5\right)\right)[/tex]
[tex]y-10=-2\left(x+5\right)[/tex]
Add 10 to both sides
[tex]y-10+10=-2\left(x+5\right)+10[/tex]
simplify
[tex]y=-2x[/tex]
Thus, the equation of the line that passes through the given points is:
Hence, option D is correct.
The graph of the line equation is also attached below.
