Question

Determine the x-int of the line that passes through (3,7) and (14,22)

Answer 1

The slope of this line is

$\dfrac{22-7}{14-3}=\dfrac{15}{11}$

Using the point-slope formula, the equation of the line is

$y-7=\dfrac{15}{11}(x-3)\implies y=\dfrac{15}{11}x+\dfrac{32}{11}$

The $x$-intercept occurs when $y=0$:

$0=\dfrac{15}{11}x+\dfrac{32}{11}\implies x=-\dfrac{32}{15}$

so that it has coordinates

$\left(-\dfrac{32}{15},0\right)$