Question

Determine the equation of the line that passes through the given points. (If you have a graphing calculator, you can use the table feature to confirm that the coordinates of both points satisfy your equation.)

(-5, 10) and (5, -10)
a.
y = 2 x minus 10
b.
y = 2 x
c.
y = negative 2 x + 20
d.
y = negative 2 x

Answer 1

The equation of the line that passes through the given points is:

• 
  `y=-2x`

Hence, option D is correct.

The graph of the line equation is also attached below.

Explanation:

Given the points

• (-5, 10)

• (5, -10)

Finding the slope between (-5, 10) and (5, -10)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(-5,\:10\right),\:\left(x_2,\:y_2\right)=\left(5,\:-10\right)`

`m=(-10-10)/(5-\left(-5\right))`

`m=-2`

Using the point-slope form to determine the line equation

Point slope form:

`y-y_1=m\left(x-x_1\right)`

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = -2 and the point (-5, 10)

`y-10=-2\left(x-\left(-5\right)\right)`

`y-10=-2\left(x+5\right)`

Add 10 to both sides

`y-10+10=-2\left(x+5\right)+10`

simplify

`y=-2x`

Thus, the equation of the line that passes through the given points is:

• 
  `y=-2x`

Hence, option D is correct.

The graph of the line equation is also attached below.