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.
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.
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