What is the equation of the line with slope # m= -3/7 # that passes through # (17/13,14/7) #?

1 Answer
KillerBunny
Jun 20, 2018

#y = -3/7x + \frac{233}{91}#

Explanation:

When you know a given point #(x_0,y_0)# and the slope #m#, the equation of a line is

#y-y_0 = m(x-x_0)#

In your case, #(x_0,y_0) = (\frac{17}{13}, \frac{14}{7}) = (\frac{17}{13},2)# and #m=-3/7#.

Let's plug these values in the formula:

#y-2 = -3/7(x-\frac{17}{13})#

Although this already is the equation of the line, you may want to write in the slope-intercept form, for example. Expanding the right hand side, we have

#y-2 = -3/7x+\frac{51}{91}#

add #2# to both sides to get

#y = -3/7x + \frac{233}{91}#

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