Question 452261: Write an equation of the line containing the given point and perpendicular to the given line.
(5,-2); 5x + 4y = 9
The equation of the line is y=_______________
(Type your answer in the form y = mx + b. Simplify your answer. Type an integer or a fraction.
Answer by confusedgirl81(14)   (Show Source):
You can put this solution on YOUR website! (5,-2); 5x + 4y = 9
We have to put this equation in slope-intercept form.
First subtract subtract 5x from both sides
4y = -5x + 9
Divide both sides by 4
y = -5/4x + 9/4
You can see m = -5/4. This is the slope.
For a line to be perpendicular to the above line, they must have a slope of 4/5, (the exact opposite of above).
Now we will use the given point (5,-2) and the slope 4/5 to write the point-slope formula.
y - (y1) = m(x - x1)
Since we know -2 = y1, 5 = x1, and 4/5 = m. Substitute it in.
y - (-2) = 4/5(x - (5))
y + 2 = 4/5(x - 5)
substitute
4(x - 5) = 5(y + 2)
Use the Distributive Property.
4x - 20 = 5y + 10
Write the equation in general form
5y = 4x - 30
Divide 5 from both sides
y = 4/5x - 30/5
Simplify
y = 4/5x - 6
y = -5/4x + 9/4 is parallel to y = 4/5x - 6
If you need more help, just ask!
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