Questions: Consider the following function. r(x) = 4(1 - 1/2 x) + 6x Find two points on the line to graph the function.

Solution Steps

To find two points on the line to graph the function \( r(x) = 4\left(1 - \frac{1}{2} x\right) + 6x \), we can choose two different values for \( x \), substitute them into the function, and calculate the corresponding \( r(x) \) values. These pairs \((x, r(x))\) will be the points on the line.

The given function is: \[ r(x) = 4\left(1 - \frac{1}{2} x\right) + 6x \]

We choose two values for \( x \): \[ x_1 = 0 \quad \text{and} \quad x_2 = 2 \]

Substitute \( x_1 = 0 \) into the function: \[ r(0) = 4\left(1 - \frac{1}{2} \cdot 0\right) + 6 \cdot 0 = 4 \] Thus, the first point is: \[ (0, 4.000) \]

Substitute \( x_2 = 2 \) into the function: \[ r(2) = 4\left(1 - \frac{1}{2} \cdot 2\right) + 6 \cdot 2 = 4(1 - 1) + 12 = 12 \] Thus, the second point is: \[ (2, 12.00) \]

Final Answer