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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

Sagot :

absor201

Answer:

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

  • [tex]y=-2x[/tex]

Hence, option D is correct.

The graph of the line equation is also attached below.

Step-by-step explanation:

Given the points

  • (-5, 10)
  • (5, -10)

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:

  • [tex]y=-2x[/tex]

Hence, option D is correct.

The graph of the line equation is also attached below.

View image absor201
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