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
Is it A?
Y = mx + b.
m = -1/15.
b = y-mx = 1-(-1/15)1 = 1 + 1/15 = 16/15.
Eq: Y = (-1/15)x + 16/15.
I don't see a match. The slope should be -1/15.
geez - give it a rest, ok ?
And fix your dang typos!
To find the equation of a line that is perpendicular to a given line and passes through a given point, you need to use the fact that the slopes of perpendicular lines are negative reciprocals of each other.
Given line: y = 15x + 45
The slope of the given line is 15.
To find the slope of the line perpendicular to the given line, take the negative reciprocal of the slope:
Perpendicular slope = -1/15
Next, use the point-slope form of a linear equation to find the equation of the line passing through the given point (1,1) with the perpendicular slope:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the perpendicular slope.
Substituting (1,1) and -1/15 into the equation:
y - 1 = (-1/15)(x - 1)
Now simplify the equation:
y - 1 = (-1/15)x + 1/15
Add 1 to both sides of the equation:
y = (-1/15)x + 1/15 + 1
Combining the constants on the right side:
y = (-1/15)x + 1/15 + 15/15
Simplifying the equation further:
y = (-1/15)x + 16/15
Comparing this equation with the given options, we can see that the correct equation is:
A) y = −5x + 6
So, the correct answer is A.