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Find the equation of the line that contains the given point and is parallel to the given line. Write the equation in slope-intercept form, if possible

(-6,4): 7x - 2y = -3
A:The equation of the parallel line in slope-intercept form is
B: The equation of the parallel line cannot be written in slope-intercept form. The equation of the parallel line is

User Rohit Goel
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Final answer:

The equation of the line parallel to 7x - 2y = -3 and passing through the point (-6,4) is y = (7/2)x + 25.

Step-by-step explanation:

To find the equation of the line that is parallel to the given line 7x - 2y = -3 and passes through the point (-6,4), we first need to determine the slope of the given line. A line with m as the slope and b as the y-intercept is expressed as y = mx + b. We can reorganize the provided line into slope-intercept form as follows:

  • 7x - 2y = -3
  • -2y = -7x - 3
  • y = (7/2)x + 3/2

Now, we see that the slope (m) is 7/2 for the given line. A parallel line will have the same slope, so our new line will also have a slope of 7/2. The equation of the line that passes through the specified point is found using the point-slope form:

  • y - y1 = m(x - x1)
  • y - 4 = (7/2)(x + 6)

Expanding this and solving for y gives us:

  • y - 4 = (7/2)x + 21
  • y = (7/2)x + 25

Thus, the equation of the parallel line in slope-intercept form is y = (7/2)x + 25.

User Boogie
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