Select the equation of a line that is perpendicular to the function graphed below:
Responses
y=−2x+3
y is equal to negative 2 x plus 3
x+2y=14
x plus 2 y is equal to 14
y+2=2(x−4)
y plus 2 is equal to 2 times open paren x minus 4 close paren
y=2x−1
To determine which equation represents a line that is perpendicular to the function graphed, we need to consider the slopes of the lines. For two lines to be perpendicular, their slopes must be negative reciprocals of each other.
Unfortunately, I can't see the graph of the function you're mentioning, but I can still show you how to assess whether each of the given lines is perpendicular to another line if you know the slope of that line.
Let's assume that the slope (m) of the unknown line is a.
1. y = −2x + 3
The slope of this line is -2. A line perpendicular to this would have a slope of the negative reciprocal, 1/2.
2. x + 2y = 14
To find the slope, rewrite as y = -1/2x + 7. The slope is -1/2. A line perpendicular to this one would have a slope of the negative reciprocal, 2.
3. y + 2 = 2(x − 4)
Simplified, this is y = 2x - 8 (after distributing the 2 and subtracting 2 from both sides). The slope is 2. A line perpendicular to this would have a slope of -1/2.
4. y = 2x − 1
The slope here is 2. Similarly, a line perpendicular to this one would have a slope of -1/2.
Now, if you know the slope of the function mentioned in your question, you would pick an equation whose slope is the negative reciprocal of that slope for it to be perpendicular to the function's graph. If you can supply the slope of the function in your question, I can immediately identify the equation that represents a perpendicular line.