SOLUTION: PLEASE EXPLAIN HOW YOU GOT THE ANSWER WRITE AN EQUATION FOR THE LINE THROUGH THE POINT (1,1) AND PERPENDICULAR TO THE LINE 2X+Y=9 THANK YOU JOHN

Question 355205: PLEASE EXPLAIN HOW YOU GOT THE ANSWER
WRITE AN EQUATION FOR THE LINE THROUGH THE POINT (1,1) AND PERPENDICULAR TO THE LINE 2X+Y=9
THANK YOU
JOHN
Found 2 solutions by Alan3354, ewatrrr:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Do it like this:
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A line and a point example.
Write in standard form the eqation of a line that satisfies the given conditions. Perpendicular to 9x+3y=36, through (1,2)
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Find the slope of the line. Do that by putting the equation in slope-intercept form, y = mx + b. That means solve for y.
9x+3y = 36
3y= - 9x + 36
y = -3x + 12
The slope, m = -3
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The slope of lines parallel is the same.
The slope of lines perpendicular is the negative inverse, m = +1/3
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Use y = mx + b and the point (1,2) to find b.
2 = (1/3)*1 + b
b = 5/3
The equation is y = (1/3)x + 5/3 (slope-intercept form)
x - 3y = -5 (standard form)
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For further assistance, or to check your work, email me via the thank you note, or at Moral Loophole@aol.com
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
Hi,
*Note: parallel lines have the same slope. (they "slant" in the same direction so they do not cross one another: they are parallel)
.
The slope intercept equation for a line is y = mx + b where m is the slope and y -intercept (the point where the line crosses the y axis)
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solving equation given for y, in order to find its slope
2X+Y = 9
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y = -2x + 9 Slope of this line is
.
Our new line also with a slope of -2 (slope is negative, both lines slope to the left)

.
substituting these values (1,1))to solve for b

b = 3
.
Equation of new line

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