No, it is not true.
Work Step by Step
There are many lines with a slope of $1$ that do not pass through the origin. The slope of a line only describes its rate of change, not its position on the graph. If a graph has a slope of $1$, it means that its $y$ is increasing at the same rate as its $x$. The line could cross the $y$-axis anywhere and have this slope, not just at the origin.