How do you find a standard form equation for the line with point (5, 0), and whose slope is -2?

1 Answer
smendyka
Feb 20, 2017

See the entire solution process below:

Explanation:

First, we can use the point-slope formula to write an equation for this line. 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 and point from the problem gives:

#(y - color(red)(0)) = color(blue)(-2)(x - color(red)(5))#

The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)#

Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1.

We can now transform the equation we obtained above into the form as follows:

#y = (color(blue)(-2)xx x) - (color(blue)(-2)xx color(red)(5))#

#y = -2x + 10#

#color(red)(2x) + y = color(red)(2x) - 2x + 10#

#2x + y = 0 + 10#

#color(red)(2)x + color(blue)(1)y = color(green)(10)#

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