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

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Answer 1 · 2015-12-30T16:59:38

In general form:

#20x - 125y + 629 = 0#

The equation of a line of slope #m# passing through a point #(x_1, y_1)# can be written in point slope form as:

#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 #29/10# to both sides we get:

#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# then we get:

#125 y = 20 x + 629#

Subtract #125y# from both sides and transpose to get:

#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.