line l and and line k are perpendicular. line l has a slope of 3. line k contains the points (5,8) and (2, y). what is the value of y?
line l has slope 3, so line k haas slope -1/3
using the point-slope form of a line,
(y-8) = -1/3 (x-5)
3y-24 = 5-x
3y = 29-x
so, if (2,y) is on the line,
3y = 29-2 = 27
y = 9
Or, without quite so much algebra, knowing that line k has slope 1/-3, we know that y increases by 1 when x decreases by 3.
going from (5,8) to (2,y), x has decreased by 3, so y increases by 1, from 8 to 9.
Well, that's certainly a puzzling question! If line l is perpendicular to line k, then their slopes are negative reciprocals of each other. Since the slope of line l is 3, we can determine the slope of line k by taking the negative reciprocal of 3, which is -1/3.
Now, line k contains the points (5,8) and (2, y). We can use the slope-intercept form of a linear equation, y = mx + b, to find the value of y. Plugging in the values, we have:
8 = (-1/3)(5) + b
Now, let's do some math!
8 = (-5/3) + b
To isolate b, we can add 5/3 to both sides:
8 + 5/3 = b
To make things easier, let's find a common denominator for the fractions:
24/3 + 5/3 = b
Now, let's simplify:
29/3 = b
Ah hah! We've got our answer! The value of y is 29/3.
To determine the value of y in line k, we need to use the fact that line l and line k are perpendicular. Perpendicular lines have slopes that are negative reciprocals of each other.
Since line l has a slope of 3, the slope of line k will be -1/3.
To find the value of y in line k, we need to use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
We are given that line k contains the points (5,8) and (2, y). Let's use the point-slope form to find the equation of line k using the point (5,8):
(y - 8) = (-1/3)(x - 5)
Now, let's substitute the x and y values from (2, y) into the equation:
(y - 8) = (-1/3)(2 - 5)
(y - 8) = (-1/3)(-3)
(y - 8) = 1
y = 1 + 8
y = 9
Therefore, the value of y in line k is 9.
To find the value of y, we first need to determine the slope of line k. Since line l and line k are perpendicular, their slopes are negative reciprocals of each other.
The slope of line l is given as 3. So, the slope of line k would be -1/3.
To find the equation of line k, we can use the point-slope form:
(y - y1) = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
We have the point (5,8) on line k. So, the equation of line k becomes:
(y - 8) = (-1/3)(x - 5)
To find the value of y, we substitute the x-coordinate of the other given point (2, y) into the equation and solve for y:
(y - 8) = (-1/3)(2 - 5)
(y - 8) = (-1/3)(-3)
(y - 8) = 1
Now, we isolate y by adding 8 to both sides of the equation:
y = 1 + 8
y = 9
Therefore, the value of y is 9.