What is the equation of the line that passes through the given point and is perpendicular to the given line?
Point: (1,1)
Line: y=15x+45
A. y=−5x+6
B. y=−5x+45
C. y=15x−15
D. y=−5x−54
I think it is A
I really need help
I suck at geo
See 6:33PM post.
if the original has slope = 15
then perpendicular has slope -1/15
That is none of the above.
You have an error in the statement.
To determine the equation of a line that is perpendicular to another line, you need to consider the slope.
The given line is y = 15x + 45. To find a line that is perpendicular to it, you need to find its negative reciprocal slope.
First, determine the slope of the given line. The given equation is in the form y = mx + b, where m represents the slope. In this case, the slope is 15.
To find the negative reciprocal slope, take the negative reciprocal of 15, which is -1/15.
Now that you have the slope, use the point (1,1) to determine the equation of the line using the point-slope form of a line: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.
Plugging in the values, we get:
y - 1 = (-1/15)(x - 1)
Next, simplify the equation:
y - 1 = (-1/15)x + 1/15
To isolate y, add 1 to both sides of the equation:
y = (-1/15)x + 1/15 + 1
Combining the constants, we get:
y = (-1/15)x + 16/15
Looking at the answer choices, we can see that the equation y = (-1/15)x + 16/15 matches option A, y = −5x + 6. Therefore, the correct answer is A.