SAT Math : How to find the equation of a perpendicular line
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Example Questions
Example Question #52 : Coordinate Geometry
Which of the following is NOT perpendicular to 
Parallel lines have slopes that are opposite reciprocals. Any line perpendicular to 
Example Question #51 : Coordinate Geometry
A vertical line is drawn to connect the x-axis and point 
The given key word is vertical. If a perpendicular line that intersects the vertical line, the slope must be zero, and the line would be a horizontal line. The horizontal line will intersect the point at 
The answer is:
Example Question #54 : Coordinate Geometry
Which of the following is perpendicular to the line 
None of the given answers
First, we want to identify the slope of our given line. In slope-intercept form, a line's slope 
The slope of our given line is 
Now, we can start to find the perpendicular line. Remember that in order for two lines to be perpendicular, their slopes must be negative reciprocals of each other.
In this case, we want to find a line whose slope is the negative reciprocal of 
With this in mind, the only answer choice with a slope of 
Therefore, the perpendicular line is
Example Question #11 : How To Find The Equation Of A Perpendicular Line
Which of the following equations represents a line that goes through the point 
In order to solve this problem, we need first to transform the equation from standard form to slope-intercept form:
Transform the original equation to find its slope.
First, subtract 
Simplify and rearrange.
Next, divide both sides of the equation by 6.
The slope of our first line is equal to 
Let's calculate the opposite reciprocal of our slope:
The slope of our line is equal to 2. We now have the following partial equation:
We are missing the y-intercept, 
Add 4 to both sides of the equation.
Substitute this value into our partial equation to construct the equation of our line:
Example Question #1 : How To Find The Equation Of A Perpendicular Line
What is the equation of a line that runs perpendicular to the line 2x + y = 5 and passes through the point (2,7)?
2x + y = 7
2x – y = 6
x/2 – y = 6
x/2 + y = 5
–x/2 + y = 6
–x/2 + y = 6
First, put the equation of the line given into slope-intercept form by solving for y. You get y = -2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½x + 6. Rearranged, it is –x/2 + y = 6.
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