A line passes through \((6,3)\), \((8,4)\), and \((n, -2)\). Find the value of \(n\).

General\ equation\ for\ line\ in\ slope\ intercept\ form:\\y=ax+b\\\\To\ find\ a\ and\ b\ substitude\ points\ (6,3),\ (8,4)\ into\ equation\\\\ \left \{ {{3=6a+b}\ \ \ \ \atop {4=8a+b\ |*-1}} \right.\\\\ \left \{ {{3=6a+b}\ \ \ \ \atop {-4=-8a-b\}} \right.\\+----\\-1=-2a\ \ |:-2\\\\a=\frac{1}{2}\\\\3=6\cdot\frac{1}{2}+b\\3=3+b\\b=3-3=0\\y=\frac{1}{2}x\\\\To\ find\ value\ of\ n\ we\ have\ to\ substitute\ (n,-2)\ to\ equation:\\\\-2=\frac{1}{2}n\ \ \ \ \ \ \ \ \ |\cdot2\\\
=-4

Answered by luana | 2024-06-10

To find the value of n for which a line passes through the points (6,3), (8,4), and (n, -2), we need to determine the slope of the line using the two given points and then use this slope to find the third point.
Step 1: Find the slope of the line
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using points (6,3) and (8,4), we get:
m = (4 - 3) / (8 - 6) = 1 / 2
Step 2: Use the slope to find n
Using the slope formula again with point (n, -2) and one of the other points, say (6,3):
1 / 2 = (-2 - 3) / (n - 6)
Solve for n:
1 / 2 = -5 / (n - 6)
n - 6 = -10
n = -4
Therefore, the value of n that makes the line pass through (n, -2) is -4.

Answered by MarlonBrando | 2024-06-24

The value of n for the point ( n , − 2 ) is − 4 . This was calculated by first finding the slope of the line passing through the points ( 6 , 3 ) and ( 8 , 4 ) , then using this slope to write the line equation and substituting y = − 2 .
;

Answered by luana | 2024-10-01