To find the equation of a line perpendicular to the given line, we'll need to determine the slope of the given line first.
Given line equation: 4x + 9y = 2.
To find the slope, we need to solve for y in terms of x. We'll put the given equation in slope-intercept form (y = mx + b), where 'm' represents the slope.
4x + 9y = 2
9y = -4x + 2
y = (-4/9)x + 2/9
The slope of the given line is -4/9.
Since a line perpendicular to another line has a negative reciprocal slope, the slope of the line perpendicular to the given line is (9/4).
Now, we can use the given point (0,8) and the perpendicular slope (9/4) to write the equation of the line.
Using the point-slope formula, the equation is:
y - y₁ = m(x - x₁)
Plugging in the values:
y - 8 = (9/4)(x - 0)
Simplifying:
y - 8 = (9/4)x
Finally, we can rewrite it as the standard equation form:
(9/4)x - y + 8 = 0
Therefore, the equation of the line containing the point (0,8) and is perpendicular to the line 4x + 9y = 2 is:
(9/4)x - y + 8 = 0
Write an equation of the line containing the given point and perpendicular to the given line.
(0,8); 4xplus9yequals2
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