math help please?

Question

1.find the value of k so that the slope of the line passing through points (5,3) and (k,6) will be 1

2.find the value of t so that the slope of the line passing through points (2,t) and (6,10) will be 1/2

Answer 1

You solve both of these the same way. use the formula for slope
m = delta y/ delta x
For the first one
m = (5 - k)/(3-6) = 1
solve this for k to get your answer.
Do the same thing for 2.

Answer 2

1.find the value of k so that the slope of the line passing through points (5,3) and (k,6) will be 1

slope=rise/run
1=(6-3)/(k-5)
1=3/(k-5) <<<<< multiply (k-5) for both sides
k-5=3
k=8


2.find the value of t so that the slope of the line passing through points (2,t) and (6,10) will be 1/2

(im gonna use 0.5 for 1/2 to make it easier to read)
slope=rise/run
0.5=(10-t)/(6-2)
0.5=(10-t)/4 <<<<< multiply both sides by 4
2=10-t
t=10-2
t=8

Answer 3

ok for number one you know the slope

slope = 1 = change in y / change in x

so 1 = y2-y1 / x2-x1

substitute

1 = 6-3 / k-5

simplify

1 = 3 / k - 5
k - 5 = 3
k =8

number 2)
same concept

.5 = 10-t / 4
2 = 10 -t
t = 8

Answer 4

6 - 3 / K - 5 = 1

3 / K - 5 = 1

K - 5 = 3

K = 8

T - 10/ 2- 6 = 1/2
T - 10 / -4 = 1/2
Cross mult.

2(T - 10) = -4
T - 10 = -2
T = 8