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Is the line through the points R(-1,3) and S(2,-7) parallel to the graph of the line given by the equation, 10x + 3y = 6? Explain.

A. yes, both lines are vertical.
B. Yes, both lines have the same slope.
C. No, both lines have positive slopes that are not equal.
D. No, both lines have negative slopes that are not equal.

Respuesta :

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Find the slope of the given two points
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Slope = (3-(-7)) / (-1 -2) = 10/-3 = - 10/3

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Find the slope of the given equation
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10x + 3y = 6
3y = -10x + 6
y = - 10/3 x + 2
Slope = -10/3

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Conclusion
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The slopes are the same, therefore the two lines are parallel.

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Answer: B Yes, both have the same slope.
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Answer:

Option B - Yes, both lines have the same slope.

Step-by-step explanation:

To find : Is the line through the points R(-1,3) and S(2,-7) parallel to the graph of the line given by the equation, [tex]10x + 3y = 6[/tex]?

Solution :

We know when lines are parallel their slopes are equal.

The slope of line through the points R(-1,3) and S(2,-7) is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-7-3}{2-(-1)}[/tex]

[tex]m=\frac{-10}{3}[/tex]

The slope of line [tex]10x + 3y = 6[/tex] is

[tex]3y=-10x+ 6[/tex]

[tex]y=\frac{-10x+ 6}{3}[/tex]

[tex]y=\frac{-10}{3}x+\frac{6}{3}[/tex]

[tex]y=\frac{-10}{3}x+2[/tex]

The slope of the line is [tex]m=\frac{-10}{3}[/tex]

Yes, both lines have the same slope.

Therefore, option B is correct.