To find the equation of the line that is parallel to the line 9x - 2y = 5, we need to determine the slope of the given line.
To do this, we can rearrange the given equation into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept of the line.
9x - 2y = 5
-2y = -9x + 5
y = (9/2)x - 5/2
From the rearranged equation, we can see that the slope of the given line is 9/2.
Since the line we are looking for is parallel to the given line, it will also have a slope of 9/2.
Now we can use the point-slope form of a linear equation to find the equation of the line that passes through the point (9,-9) with a slope of 9/2.
The point-slope form is given by:
y - y₁ = m(x - x₁)
Using the given point (9,-9) and a slope of 9/2, the equation becomes:
y - (-9) = (9/2)(x - 9)
Simplifying this equation:
y + 9 = (9/2)(x - 9)
Distributing (9/2) to (x - 9):
y + 9 = (9/2)x - 81/2
Moving 9 to the right side of the equation:
y = (9/2)x - 81/2 - 9
y = (9/2)x - 81/2 - 18/2
y = (9/2)x - 99/2
Therefore, the equation of the line that contains the point (9,-9) and is parallel to the line 9x - 2y = 5 is y = (9/2)x - 99/2.
Write an equation of the line containing the given point and parallel to the given line. Solve for y.
(9, -9); 9x - 2y = 5
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