How do you find an equation of the straight line passing through the points with coordinates (-1,5) and (4,-2), giving your answer in the form ax+by+c=0?

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Answer 1 · 2016-11-02T08:45:42

Please see the explanation for details regarding how one does the requested process.

The definition of the slope, m, of the line between two points, #(x_1,y_1)# and #(x_2,y_2)# is:

#m = (y_2 - y_2)/(x_2 - x_1)#

Using the given points to compute m:

#m = (-2 - 5)/(4- -1) = -7/5#

The slope-intercept form of the equation of a line is:

#y = mx + b#

Using the slope and the point #(-1,5)#, allows us to substitute -1 for x, 5 for y, and #-7/5# for m, so that we may find the value of b:

#5 = -7/5(-1) + b#

#5 = 7/5 + b#

#5 - 7/5 = b#

#25/5 - 7/5 = b#

b = 18/5

The slope-intercept form of the line that goes through the two given points is:

#y = -7/5x + 18/5#

But we want the form, #ax + by + c = 0#, multiply boths side by 5:

#5y = -7x + 18#

Add #7x - 18# to both sides:

#7x + 5y - 18 = 0#