What is the equation of the line between #(3,-2)# and #(5,1)#?

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Answer 1 · 2018-05-30T12:43:44

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)(1) - color(blue)(-2))/(color(red)(5) - color(blue)(3)) = (color(red)(1) + color(blue)(2))/(color(red)(5) - color(blue)(3)) = 3/2#

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 calculated above and the values from the first point in the problem gives:

#(y - color(blue)(-2)) = color(red)(3/2)(x - color(blue)(3))#

#(y + color(blue)(2)) = color(red)(3/2)(x - color(blue)(3))#

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

#(y - color(blue)(1)) = color(red)(3/2)(x - color(blue)(5))#

Answer 2 · 2018-05-30T12:44:22

#y=3/2x-13/2#

#m=(y_2-y_1)/(x_2-x_1)=(1+2)/(5-3)=3/2#
So
#y=3/2x+n#
we have
#1=15/2+n#

so

#n=-13/2#