Chapter 1, Problem 1MC

Determine whether each of the following statements is true or false.

The x-intercept of the line that passes through $\left(-\frac{2}{3},\frac{3}{2}\right)$ and the origin is $\left(-\frac{2}{3},0\right)$. [1.1]

To determine

Whether the given statement is true or false.

Answer to Problem 1MC

The given statement is false.

Explanation of Solution

Given:

The statement “The x-intercept of the line that passes through $\left(\frac{-2}{3},\frac{3}{2}\right)$ and the origin is $\left(\frac{-2}{3},0\right)$”.

Calculation:

From the given statement the line passes through the two points $\left(\frac{-2}{3},\frac{3}{2}\right)$ and $\left(0,0\right)$.

Obtain the graph of the line with the above conditions as shown below in Figure 1.

From, Figure 1, it is observed that the line does not passes through the point $\left(\frac{-2}{3},0\right)$ and $\left(0,0\right)$ is the only one x-intercept.

Thus, the given statement is false.