I need help with a question...
In this case k and l are parallel lines and contain the given points of: k=(2,5),(8,14) and l=(5,3),(11,y)... how do I calculate for y?
Please help!
I hope you are not taught to use a notation like
k=(2,5),(8,14)
to represent a line through those two points, anyway ...
the slope of the first line is (14-5)/(8-2) = 3/2
the slope of the second line is (y-3)/(11-5) = (y-3)/6
but parallel lines have equal slopes, so ...
(y-3)/6 = 3/2
2y-6 = 18
2y=24
y=12
y = 33/2
To calculate the value of y in this scenario, we can use the concept of parallel lines.
When two lines are parallel, their slopes are equal. So, to find the value of y, we need to find the equation of line l and then equate its slope with the slope of line k.
First, we find the slope of line k using the formula: slope = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points on line k.
Using the points (2,5) and (8,14) from line k, we substitute the values into the slope formula: slope_k = (14 - 5) / (8 - 2).
Calculating the slope of line k, we get: slope_k = 9 / 6 = 3/2.
Now, we find the equation of line l using the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Using the point (5,3) on line l and the slope calculated from line k, we substitute the values into the point-slope form: y - 3 = (3/2)(x - 5).
Expanding and simplifying the equation, we get: y - 3 = (3/2)x - 15/2.
To isolate y, we add 3 to both sides of the equation: y = (3/2)x - 15/2 + 3.
Simplifying further, we get: y = (3/2)x - 15/2 + 6/2.
Combining the fractions, we have: y = (3/2)x - 9/2.
So, the equation for line l is y = (3/2)x - 9/2.
Now that we have the equation of line l, we can substitute the x-coordinate of the given point (11, y) into the equation and solve for y. Plugging in x = 11, we have: y = (3/2)(11) - 9/2.
Calculating further, we get: y = 33/2 - 9/2 = 24/2 = 12.
Therefore, the value of y in the point (11, y) on line l is 12.