What is an equation of the line that passes through the point (6, -8) and is parallel to the line x + 2y = 6?
What is an equation of the line that passes through the point (6, -8) and is parallel to the line x + 2y = 6?
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info@snapandsolve.comTo find the equation of a line parallel to x + 2y = 6, we first need to determine the slope of the given line. The equation x + 2y = 6 can be rewritten in slope-intercept form (y = mx + b) as 2y = -x + 6, or y = -1/2x + 3. The slope (m) is -1/2.
Since parallel lines have the same slope, the line we are looking for also has a slope of -1/2. Using the point-slope form of a line equation, y - y₁ = m(x - x₁), where (x₁, y₁) is the point (6, -8), we have:
y + 8 = -1/2(x - 6)
Expanding this, we get:
y + 8 = -1/2x + 3
y = -1/2x - 5
Thus, the equation of the line is y = -1/2x - 5.
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