How do you find t if the slope is 5/2 and the coordinates are (-1, 4) and (4, t)?

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Answer 1 · 2016-05-24T11:43:47

#t=41/4 -> 10 1/4#

Slope (gradient) is the relationship between the change in the up/down compared to the change in along

Let point 1 be #P_1->(x_1,y_1)->(-1,4)#
Let point 2 be #P_2->(x_2,y_2)(->(4,t)#

The gradient is given as #5/2#

#("Change in y")/("Change in x")=5/2 = (y_2-y_1)/(x_2-x_1)#

So

#5/2=(t-4)/(4-(-1)) = (t-4)/5#

#5/2=(t-4)/5#

Multiply both sides by 5

#5xx5/2=(t-4)xx5/5#

But #5/5=1#

#25/2=t-4#

Add 4 to both sides

#t=25/4+4#

#t=41/4#