The equation of a line that passes through the points (3,7) and (5,3). Leave your answer in the form ? y=mx+c

1 Answer
NJ
Apr 18, 2018

#=>y = -2x + 13#

Explanation:

You can use point-slope form to determine the slope #m#:

#y_2 - y_1 = m(x_2-x_1)#

Given:

#=> p_1 = (x_1,y_1) = (3,7)#
#=>p_2=(x_2,y_2) = (5,3)#

Finding the slope:

#3-7 = m(5-3)#

#-4 = 2m#

#=>m = -2#

To write an equation of a line in intercept form, simply choose either of the two points and use the slope found. This works for either point, as both points lie on the line. Let's use the first point #(3,7)#.

#y - 7 = -2(x - 3)#

#y - 7 = -2x + 6#

#=>color(blue)(y = -2x + 13)#

Just to show the other point works too #(5,3)#.

#y - 3 = -2(x - 5)#

#y - 3 = -2x + 10#

#y = -2x + 13#

we arrived at the same answer.

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