Question

State whether each sentence is true or false. If false, replace the underlined word or number to make a true sentence.

The graph of any direct variation equation passes through $\left(0,1\right)$.

Short answer

False. The graph of any direct variation equation passes through $\left(0,0\right)$.

Step-by-step solution

Step 1. State the equation of a straight line.

The standard form of a straight line is given by, $y=mx+c$, where, m is the slope of the line and c is the y-intercept. The graph of direct variation equation is a line passing through the origin.

Step 2. Find the point where any direct variation graph passes.

The origin is at $\left(0,0\right)$. Since, the direct variation equation is the equation of a straight line passing through the origin. The graph must passes through the point $\left(0,0\right)$.

Step 3. Conclusion.

It is false because the graph of any direct variation equation passes always through point $\left(0,0\right)$.