What is an equation of the line that passes through the point (2, 6) and is perpendicular to the line x +...
What is an equation of the line that passes through the point (2, 6) and is perpendicular to the line x + 4y = 8?
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info@snapandsolve.comTo find the equation of the line, we first need to determine the slope of the given line x + 4y = 8. Rewrite it in slope-intercept form (y = mx + b):
x + 4y = 8
4y = -x + 8
y = -1/4x + 2
The slope (m) of this line is -1/4. A line perpendicular to this will have a slope that is the negative reciprocal. Therefore, the perpendicular slope is 4.
Using the point-slope form of a line equation, y - y₁ = m(x - x₁), where (x₁, y₁) is the point (2, 6) and m is 4:
y - 6 = 4(x - 2)
y - 6 = 4x - 8
y = 4x - 2
Thus, the equation of the line is y = 4x - 2.
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