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What is the equation of a line that passes through the point (5, -1) and is parallel to the line whose equation is 2x + 5y = 1?

User Kilby
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Final answer:

To find a line parallel to 2x + 5y = 1 that passes through (5, -1), first find the slope from the original equation, which is -2/5. Then use the point to determine the y-intercept of the new line. The equation of the new line is y = (-2/5)x + 1.

Step-by-step explanation:

The equation of a line parallel to another can be found by ensuring they have the same slope. Given the equation 2x + 5y = 1, we first need to rewrite it in slope-intercept form y = mx + b, where m is the slope. To do this, we solve for y:

  • 5y = -2x + 1
  • y = (-2/5)x + 1/5

Here the slope m is -2/5. A line that is parallel to this will have the same slope. So the new equation will have the form y = (-2/5)x + b. We can find b, the y-intercept, by plugging in the coordinates (5, -1) given in the question:

  • -1 = (-2/5)(5) + b
  • -1 = -2 + b
  • b = 1

Therefore, the equation of the line that passes through the point (5, -1) and is parallel to the original line is y = (-2/5)x + 1.

User Ropeladder
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