When a line is perpendicular to another, it means that the slope is a negative reciprocal of the original. A negative reciprocal is the reciprocal and the opposite of a number. For example, the negative reciprocal of 4 is -1/4.
The slope of the original line is 1. Therefore the slope of the line that is perpendicular to it is -1/1 or -1.
Now all you need to figure out is the y-intercept. Since you know the two coordinates of the new line and its slope, you can work backwards using the slope formula to find the coordinates of the y-intercept. This may seem difficult, since you would technically have to find two coordinates but you already know one of the coordinates of the y-intercept; the x-coordinate of a y-intercept is always 0.
Therefore, all you need to figure out is the y coordinate:
slope = y2-y1/x2-x1
-1 = 3-y/-6
6 = 3-y
(subtract 3 - move it to other side)
3 = -y
y = -3
Since the slope is -1 and y-intercept is -3, you can now write the formula in slope-intercept form:
y = -x -3
If you need to write this in standard, just remember that the x cannot be negative so everything on the right side of the equal sign must move to the left. In standard form, everything is always on one side, it's just a matter of knowing what to move where.
Standard form: y + x + 3 = 0
You can always check your answer using either form of the equation by substituting the x in the formula with the x coordinate and the y with the y-coordinate and making sure the equation is true:
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When a line is perpendicular to another, it means that the slope is a negative reciprocal of the original. A negative reciprocal is the reciprocal and the opposite of a number. For example, the negative reciprocal of 4 is -1/4.
The slope of the original line is 1. Therefore the slope of the line that is perpendicular to it is -1/1 or -1.
Now all you need to figure out is the y-intercept. Since you know the two coordinates of the new line and its slope, you can work backwards using the slope formula to find the coordinates of the y-intercept. This may seem difficult, since you would technically have to find two coordinates but you already know one of the coordinates of the y-intercept; the x-coordinate of a y-intercept is always 0.
Therefore, all you need to figure out is the y coordinate:
slope = y2-y1/x2-x1
-1 = 3-y/-6
6 = 3-y
(subtract 3 - move it to other side)
3 = -y
y = -3
Since the slope is -1 and y-intercept is -3, you can now write the formula in slope-intercept form:
y = -x -3
If you need to write this in standard, just remember that the x cannot be negative so everything on the right side of the equal sign must move to the left. In standard form, everything is always on one side, it's just a matter of knowing what to move where.
Standard form: y + x + 3 = 0
You can always check your answer using either form of the equation by substituting the x in the formula with the x coordinate and the y with the y-coordinate and making sure the equation is true:
Checking with slope-intercept equation:
y = -x -3
3 = (-1)(-6)-3
3 = 6-3
3 = 3
Checking with standard equation:
y + x + 3 = 0
3 - 6 + 3 = 0
0 = 0
Hope this helps! :)
y = -x + b , plug (-6,3) to find value of b