How do you write the equation of a line with points (-8,14), (-20,17)?

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Answer 1 · 2016-12-13T22:08:54

#y - 14 = -1/4(x + 8) or #y = -1/4x + 12#

To find the equation for these two points we must first determine the slope of the line.

The slope can be found by using the formula:

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

Where #m# is the slope and #(x_1, y_1)# and #(x_2, y_2)# are the two points.

Substituting the points we are give allows us to calculate the slope as:

#m = (17 - 14)/(-20 - -8)#

#m = 3/(-20 + 8)#

#m = -3/12#

#m = (3/3) xx (-1/4)#

#m = 1 xx (-1/4)#

# m = -1/4#

Now, we can use the point-slope formula to find the equation for the line. The point-slope formula states:

#(y - y_1) = m(x - x_1)#

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

We can substitute the slope we calculated earlier and one of the points to obtain our equation for the line:

#y - 14 = -1/4(x - -8)#

#y - 14 = -1/4(x + 8)

Or solving for #y# to put the equation into slope intercept form gives:

#y - 14 = -1/4x + -1/4 xx 8#

#y - 14 = -1/4 x - 8/4#

#y - 14 = -1/4x - 2#

#y - 14 + 14 = -1/4x - 2 + 14#

#y - 0 = -1/4x + 12#

#y = -1/4x + 12#