Write the equation of the line which passes through (2, 1) and is perpendicular to x = –2. (1 point)?
need help understanding this equation step by step
but i need help solving it step by step
- 8 years agoFavorite Answer
Hi there --
Two things to keep in mind when solving these -- first is how to find the equation of a line, given its slope and point on the line; second how to find the slopes of perpendicular lines.
In this problem, we need to recognize that the slope of x = -2 is undefined, as it's a vertical line. This means that its slope which is generally known to be the negative reciprocals (for defined nonzero numbers) ends up being zero for the case of a line with undefined slope. All this means is that lines perpendicular to a vertical line are always horizontal and, therefore, have slope m = 0.
Given this slope, now derive the equation of the line from slope-intercept form:
y = mx + b,
using m = 0, and the point (2,1) as an instance of x, y -- to find b:
1 = 0*1 + b;
so b = 1.
Thus our equation is y = 0x + 1 or just y = 1.
I put together a short video tutorial which further illustrates this solution, and cited it as a source below. We hope it is helpful.
- Bob BLv 78 years ago
The line for the equation x = -2 is a vertical line that's drawn two units to the left of the y-axis.
A line perpendicular to that one must be horizontal.
A horizontal line passing through point (2, 1) has a constant y value of 1. Its equation is:
y = 1
- BrendaLv 78 years ago
because your line is x=-2 , which is a vertical line , then the perpendicular line to it has to be an horizontal line which means y=k
because the given point is (2,1) , then the line perpendicular to x=-2 is y=1
- Iggy RockoLv 78 years ago
x = -2 is a vertical line so we want a horizontal line through (2, 1). That line is y = 1.
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- 8 years ago
Exactly what Iggy said!