How do you write an equation of the line that passes through the given points (0,0), (4,-20)?

1 Answer
smendyka
Feb 12, 2017

#(y + color(red)(20)) = color(blue)(-5)(x - color(red)(4))#

Or

#y = -5x#

Explanation:

The point-slope formula can be used to write an equation for this line. First, we must determine the slope. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#

Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.

Substituting the values from the two points in the problem gives:

#m = (color(red)(-20) - color(blue)(0))/(color(red)(4) - color(blue)(0))#

#m = (-20)/4 = -5#

The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#

Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.

Substituting the slope we calculated and the second point gives:

#(y - color(red)(-20)) = color(blue)(-5)(x - color(red)(4))#

#(y + color(red)(20)) = color(blue)(-5)(x - color(red)(4))#

We can also substitute the slope we calculated and the first point giving:

#(y - color(red)(0)) = color(blue)(-5)(x - color(red)(0))#

#y = -5x#

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