# At what point does the line (3,4) (6,5) cross the X axis?

Jun 6, 2018

Crossing point on x-axis is $\left(- 9 , 0\right)$

#### Explanation:

The slope of the line passing through $\left(3 , 4\right) \mathmr{and} \left(6 , 5\right)$ is

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{5 - 4}{6 - 3} = \frac{1}{3}$

The equation of line passing through $\left(3 , 4\right)$ having slope of

$m = \frac{1}{3}$ is $y - {y}_{1} = m \left(x - {x}_{1}\right) \mathmr{and} y - 4 = \frac{1}{3} \left(x - 3\right)$. or

$3 y - 12 = x - 3 \mathmr{and} x - 3 y = - 9$ Therefore, the equation of

line is $x - 3 y = - 9$ . When it crosses x-axis the y coordinate

is $0 \therefore x - 3 \cdot 0 = - 9 \mathmr{and} x = - 9$ Therefore ,crossing point on

x-axis is $\left(- 9 , 0\right)$

graph{x - 3 y = -9 [-10, 10, -5, 5]}