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
1.y=−5x+6
2.y=−5x+45
3.y=15x−15
4.y=−5x−54
k is right
You clearly have a typo. I suspect that the give line is y = 1/5 x + 4/5
the given line has slope 1/5
so, you want a line with slope -5 that goes through (1,1)
So, its equation is y-1 = -5 (x-1)
y = -5x + 6
So it appears you are correct.
Learn to type in fractions; cut and paste does not always work well here.
the answer is y=-5x+6 i just took the test
k is right. Just telling you for reassurance
Haha, hold on tight, my friend! To find the equation of a line that is perpendicular to another line, we need to determine the negative reciprocal of the slope of the original line. So, in this case, the slope of the original line is 15. The negative reciprocal of 15 is -1/15. Now plug in the given point (1,1) into the point-slope form y - y1 = m(x - x1), where m is the negative reciprocal of the slope and (x1, y1) is the given point. So, using some mathematical clown magic, we get the equation y - 1 = -1/15(x - 1). Simplifying that equation will give you option 3: y = 15x - 15. So, in clown terms, the equation of the line that passes through (1,1) and is perpendicular to y = 15x + 45 is y = 15x - 15.
To find the equation of a line that is perpendicular to a given line and passes through a given point, you can use the fact that perpendicular lines have slopes that are negative reciprocals of each other.
Given that the line is y = 15x + 45 and the point is (1,1), we can start by finding the slope of the given line. The slope-intercept form of a line is y = mx + b, where m represents the slope. In this case, the slope of the given line is 15.
Now, to find the slope of the perpendicular line, we take the negative reciprocal of 15. The negative reciprocal of any number is its negative value flipped upside down. Thus, the negative reciprocal of 15 is -1/15.
Next, we use the point-slope form of a line, which is y - y₁ = m(x - x₁), where (x₁, y₁) is the given point. Plugging in the values (1,1) for (x₁, y₁) and -1/15 for m, we get:
y - 1 = -1/15(x - 1)
To simplify further, we can multiply through by 15 to get rid of the fraction:
15(y - 1) = -1(x - 1)
Expanding the equation:
15y - 15 = -x + 1
Rearranging the equation to slope-intercept form:
15y = -x + 16
Dividing through by 15:
y = -1/15x + 16/15
Therefore, the equation of the line that passes through the given point and is perpendicular to the given line is option 2: y = -5x + 45.