a line passes through (6,3),(8,4), and (n,-2) find value of n
If points are all on the same line, then the slope has to be the same no matter what two points we use.
Take the first two points and find the slope. change in y/change in x
4 - 3 divided by 8 - 6
1/2 so the slope is 1/2
Now, set 1/2 equal to the slope equation that you create using the third point and one of the other two points. solve for n.
-2 -4 divided by n -8
-6/(n-8) = 1/2
can you finish it from here by cross multiplying and solving for n?
slope = (4-3)/(8-6) = 1/2
1/2 = (-2-4)/(n-8)
n-8 = -12
n = - 4
Whew, we agree :)
This is really helpful!
I wish I had this help when I was a kid.
Now I have to help my kids with homework ,and it's been 20 years so you have to refresh you memory.
Thank You!
To find the value of n, we need to determine the equation of the line passing through the given points (6,3), (8,4), and (n,-2).
The equation of a straight line can be found using the slope-intercept form, which is given by:
y = mx + b
Where m represents the slope of the line, and b represents the y-intercept.
Step 1: Find the slope (m) of the line:
The slope (m) is determined using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (6,3) and (8,4):
m = (4 - 3) / (8 - 6)
= 1 / 2
Step 2: Find the y-intercept (b) of the line:
Now that we have the slope (m), we can substitute this value and one of the given points into the equation to solve for b.
Using the point (6,3) and the slope (m=1/2):
3 = (1/2) * 6 + b
3 = 3 + b
b = 3 - 3
b = 0
Step 3: Write the equation of the line in slope-intercept form:
Now that we have both the slope (m) and the y-intercept (b), we can write the equation of the line as:
y = (1/2)x + 0
Simplifying, we have:
y = (1/2)x
Step 4: Substitute the x-coordinate and y-coordinate of the third point (n,-2) into the equation of the line and solve for n:
-2 = (1/2)n
To solve for n, we can multiply both sides of the equation by 2:
2(-2) = 2 * (1/2)n
-4 = n
Therefore, the value of n is -4.
Thus, the line passes through the points (6,3), (8,4), and (-4,-2).