Question

1. the following table gives the values of the current flowing through a certain resistor as the voltage is changed.

(a) what is the slope of the line that goes through these points?
(b) what is the equation of the line that goes through these points?
(c) what is the v-intercept of this line?

Explanation:

Plot the data points to check linearity

Using the Data Point Plotting knowledge point
The coordinates \((V, I)\) are:

$$ (10, 0.5), (20, 1.2), (40, 2.6), (60, 4.0), (80, 5.4), (100, 6.8) $$

Calculating consecutive slopes:

$$
LATEXBLOCK0
$$

Since all consecutive slopes are equal, the points lie exactly on a straight line.

Determine the slope of the line

Using the Slope Formula knowledge point

$$ m = \frac{I_2 - I_1}{V_2 - V_1} = \frac{1.2 - 0.5}{20 - 10} = 0.07\text{ A/V} $$

Find the equation of the line

Using the Point-Slope Form knowledge point

$$
LATEXBLOCK1
$$

Find the V-intercept of the line

Using the y-intercept knowledge point
To find the \(V\)-intercept, set \(I = 0\):

$$
LATEXBLOCK2
$$

Answer:

(a) The slope of the line is \(0.07\text{ A/V}\).

(b) The equation of the line is \(I = 0.07V - 0.2\).

(c) The \(V\)-intercept of the line is \(\frac{20}{7}\text{ V}\) (or approximately \(2.86\text{ V}\)).