# What is the slope-intercept form of the line passing through  (-1, 4)  and  (-4, 2)?

Feb 18, 2016

The line's equation is:
$y = \left(\frac{2}{3}\right) x + \left(\frac{14}{3}\right)$

Hence the y-axis intercept is 14/3
and the slope is 2/3.

#### Explanation:

slope = change in y / change in x

For points on the line at: (-1,4) and (-4,2)
change in y = 4 - 2 = 2
change in x = (-1) - (-4) = 3

Therefore:
slope = m = 2/3

The equation for a line is:
y = m x + c
Where c is the y-axis intercept.
Taking the first point, where x= -1 and y=4.
4 = (2/3) (-1) + c
c = 4 + (2/3) = 14/3

The line's equation is:
$y = \left(\frac{2}{3}\right) x + \left(\frac{14}{3}\right)$