# What is the equation of the line with slope # m= 4/25 # that passes through # (12/5 29/10) #?

##### 1 Answer

Dec 30, 2015

In general form:

#20x - 125y + 629 = 0#

#### Explanation:

The equation of a line of slope

#y - y_1 = m(x - x_1)#

So in our example, we can write:

#color(blue)(y - 29/10 = 4/25 (x - 12/5))#

Multiplying this out and adding

#y = 4/25 x - 48/125 + 29/10#

#= 4/25 x - 96/250 + 725/250#

#= 4/25 x + 629/125#

The equation:

#color(blue)(y = 4/25 x + 629/125)#

is in slope intercept form.

If we multiply both sides by

#125 y = 20 x + 629#

Subtract

#color(blue)(20x - 125y + 629 = 0)#

This is the general form of the equation of a line, which can cope with lines of any slope.