41

 PAGE: 193 SET: Exercises PROBLEM: 41

Observe the graph :

The line passing through the points and .

Find the constant of variation of the equation:

The statement varies directly as , means that when increases,  increases by the same factor.

Hence and always have the same ratio.

The constant of variation of the equation and the slope of the line have the same value.

(Direct variation formula)

Consider the point is .

(Substitute )

(Simplify)

Therefore, the constant of direct variation of the equation is .

Find the slope :

.

(Formula for slope)

(Substitute and )

(Simplify)

(Simplify)

Therefore, the slope is .

The constant of variation is .

The slope is .

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