# Using the point-slope form of a line, how do you find the equation of the line that passes through the point (2,1) with slope -2/3? Would the X-intercept be 3 or 3.5? and then the slope...I just need help. Thank you all for the help?

Mar 30, 2015

Rememebering the formula, that gives the equation of a line, given a point and a slope:

$y - {y}_{p} = m \left(x - {x}_{p}\right)$.

So:

$y - 1 = - \frac{2}{3} \left(x - 2\right) \Rightarrow y = - \frac{2}{3} x + \frac{4}{3} + 1 \Rightarrow$

$y = - \frac{2}{3} x + \frac{7}{3}$.

The y-intercept is $\frac{7}{3}$.

For the x-intercepet we have to solve the system:

$y = - \frac{2}{3} x + \frac{7}{3}$

$y = 0$.

So:

$0 = - \frac{2}{3} x + \frac{7}{3} \Rightarrow \frac{2}{3} x = \frac{7}{3} \Rightarrow x = \frac{7}{3} \cdot \frac{3}{2} = \frac{7}{2} = 3.5$.