How do you find the equation of the line #(20,2)# and #(32,- 4)#?

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Answer 1 · 2018-05-29T17:44:25

See a solution process below:

First, we need to determine the slope of the line. The formula for find the slope of a line is:

#m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#

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

Substituting the values from the points in the problem gives:

#m = (color(red)(-4) - color(blue)(2))/(color(red)(32) - color(blue)(20)) = -6/12 = -1/2#

Now, we can use the point-slope formula to write an equation for the line. The point-slope form of a linear equation is:

#(y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))#

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

Substituting the slope we calculate and the values from the first point in the problem gives:

#(y - color(blue)(2)) = color(red)(-1/2)(x - color(blue)(2))#

We can also substitute the slope we calculate and the values from the second point in the problem giving:

#(y - color(blue)(-4)) = color(red)(-1/2)(x - color(blue)(32))#

#(y + color(blue)(4)) = color(red)(-1/2)(x - color(blue)(32))#