find the vaule of t so that the slppe of the line passing through the points (2,t) and (6,10) will be 1/2
(t-10)/(2-6) = 1/2
(t-10)/(-4) = 1/2
2t-20 = -4
2t = 16
t = 8
thank you~
To find the value of t, we will first calculate the slope of the line passing through the points (2, t) and (6, 10), and then equate it to the desired slope, which is 1/2.
The formula to calculate the slope between two points (x1, y1) and (x2, y2) is:
slope = (y2 - y1) / (x2 - x1)
Let's substitute the given points into the formula:
slope = (10 - t) / (6 - 2) = (10 - t) / 4
Now we have the slope in terms of t. To find the value of t, we need to set this expression equal to 1/2:
(10 - t) / 4 = 1/2
To solve for t, we can cross-multiply:
2(10 - t) = 4
20 - 2t = 4
Now, isolate the variable t by subtracting 20 from both sides:
-2t = 4 - 20
-2t = -16
Finally, divide both sides by -2 to solve for t:
t = (-16) / (-2)
t = 8
Therefore, the value of t that satisfies the condition is 8.