4. The line AB passes through the points A (k, 3) and (5, 4).The gradient of AB is 1/3 Find the value of k

answer is

k=2

Step-by-step explanation:

For this type of question let's use an equation that's are used to find the slope.

Now, substitute the numbers we have,

To check your answer,

m= 4-3/5-2

m=1/3

BOOM!

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the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

(-1,-0.5)

step-by-step explanation: