Math

QuestionFind the linear function C=aI+bC=a I+b with given points, then identify which graph is parallel to it from the options.

Studdy Solution

STEP 1

Assumptions1. The consumption C is a linear function of income I, given by C = a + b. . When I = R500, C = R550.
3. When I = R1000, C = R800.
4. The graph of this linear function is parallel to one of the given options.

STEP 2

We need to find the slope of the line representing the relationship between C and I. The slope of a line is given by the change in y (C in this case) divided by the change in x ( in this case).
lope=ChangeinCChangeinIlope = \frac{Change\, in\, C}{Change\, in\, I}

STEP 3

Plug in the given values for the change in C and the change in I to calculate the slope.
lope=R800R550R1000R500lope = \frac{R800 - R550}{R1000 - R500}

STEP 4

Calculate the slope.
lope=R250R500=0.lope = \frac{R250}{R500} =0.

STEP 5

The slope of the line is0.5. This means the coefficient of I in the linear function C = a + b is0.5.

STEP 6

Now, we need to find the function among the given options that has the same slope. The slope of a line represented by the equation C = m + n is m.

STEP 7

By comparing the slopes, we find that the function with the same slope is C=0.5+10C =0.5 +10.So, the graph of the given linear function is parallel to the graph of C=0.5+10C =0.5 +10.
The answer is option b. C=0.5+10C =0.5 +10.

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