Question

State True or False:
The line $y=3x+4$ does not intersect $x$-axis.

Answer 1

Given equation of line is $y=3x+4$ ........ $\left(i\right)$

If any line intersects with $x$-axis, it has point of intersection in the form of $(x,0)$.

That is, $y$-coordinate will be $0$ at point point.

Therefore, we get the point of intersection of any line with $x$-axis by substituting $y=0$

Let $y=0$ in equation $\left(i\right)$ we get

$3x+4=0⟹x=-\frac{4}{3}$

Thus, the line in $\left(i\right)$ intersects $x$-axis at the point $(0,-\frac{4}{3})$

Hence, the given statement is false.