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Write an equation of the line passing through the point (-10, 3) that is parallel to the line 5x - 2y = 12?

User Alextes
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Final answer:

To find the equation of a line parallel to 5x - 2y = 12 that passes through (-10, 3), first determine the slope, which is 5/2. Use the point-slope form with this slope and the given point to find the new line's equation: y = (5/2)x + 28.

Step-by-step explanation:

The equation of the line passing through the point (-10, 3) that is parallel to the line 5x - 2y = 12 can be found by determining the slope of the given line and using the point-slope form of a linear equation.

Step-by-step solution:

  1. First, rearrange the given equation in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
  2. To find the slope of the given line, solve the equation for y to get y = (5/2)x - 6. The slope of the given line is 5/2.
  3. Since the line we want to find is parallel, it will have the same slope. Therefore, the slope of the line we want to find is also 5/2.
  4. Now, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
  5. Plugging in (-10, 3) as the point and 5/2 as the slope, we have y - 3 = (5/2)(x - (-10)).
  6. Simplifying the equation, we get y - 3 = (5/2)(x + 10).
  7. Expanding the right side of the equation, we have y - 3 = (5/2)x + 25.
  8. Finally, rearrange the equation to get the slope-intercept form, which is y = (5/2)x + 28.

Therefore, the equation of the line passing through the point (-10, 3) and parallel to the line 5x - 2y = 12 is y = (5/2)x + 28.

User Mypetlion
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