# How do you find another point on each line using slope and point given m=2/5; passes through (1,-4)?

Sep 4, 2016

You have to use the equation of the straight line with slope $m$ and intercept $b$, $y = m x + b$

#### Explanation:

Since $m = \frac{2}{5}$ is given, the equation of the straight line given is $y = \frac{2}{5} x + b$, where we have to still find $b$. But we know that the line passes through the point (1,-4)), so the coordinates of the point satisfy the line equation. That is:

$- 4 = \frac{2}{5} \cdot 1 + b$, and from this we know that $b = - 4 - \frac{2}{5} = - \frac{22}{5}$

Thus the line equation is

$y = \frac{2}{5} x - \frac{22}{5}$, and any point which coordinates satisfy the equation is on the line. For example if $x = 2$ then $y = \frac{2}{5} \cdot 2 - \frac{22}{5} = - \frac{18}{5}$, so we know that the point $\left(2 , - \frac{18}{5}\right)$ is also on the line. Similarly $\left(3 , - \frac{16}{5}\right)$ is on the line, etc.