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1. the equation of the line that is parallel to the line and goes through the place where it intersects it at (8, -4)  is  mathematically given as

   x – 4y = 12 is x – 4y = – 8.

   What is an equation of the line that passes through the point (8,-4)(8,−4) and is parallel to the line x-4y=12x−4y=12?

   If the slopes of two lines, m1 and m2, are equal, then the lines are parallel; if the slopes are not equal, then the lines are perpendicular.

   In the question, we are asked for the equation of the line that is parallel to the line x – 4y = 12 and goes through the place where it is represented by the coordinates (8, -4).

   The given line can be shown as:

   x – 4y = 12,

   We may determine the slope of the line by comparing it to its slope-intercept form, which is written as y = mx + b. The slope of the line is 1/4.

   The slope, m = 1/4, will also be present on the line that is parallel to this one. The necessary line goes through the location in question (8, -4).

   Considering the one-point formula, (y – y₁) = m(x – x₁), we can write the required equation as:

   y – (-4) = (1/4)(x – 8),

   Therefore

   x – 4y = – 8.

   In conclusion, the equation of the line that is parallel to the line and goes through the place where it intersects it at (8, -4) x – 4y = 12 is x – 4y = – 8.

   Learn more about parallel lines at

   brainly.com/question/13763238

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