How do you write an equation in point slope form given (–1, 3) and (1, 7)?

2 Answers
Mark D.
Apr 11, 2018

I don't know what " point slope form" is but here's the equation
#y=2x+5#

Explanation:

If we have two points (-1,3) and (1,7) we can find the gradient (slope). We do this by finding the difference between the two
#y# values and divide this by the difference between the two #x# values

7-3=4 this is the difference in the #y# values

1--1=1+1=2 #=># difference in #x# values

Gradient #=4/2# =2

The equation of the line is #y=2x+c# where the c value is the #y# intercept.( the place it crosses the #y# axis)

Substitute (1,7) into the equation to find c

7=#2xx1#+c

7=2+c

5=c

Put this into the equation in place of c

Jim G.
Apr 11, 2018

#y-7=2(x-1)#

Explanation:

#"the equation of a line in "color(blue)"point-slope form"# is.

#•color(white)(x)y-y_1=m(x-x_1)#

#"where m is the slope and "(x_1,y_1)" a point on the line"#

#"to calculate m use the "color(blue)"gradient formula"#

#•color(white)(x)m=(y_2-y_1)/(x_2-x_1)#

#"let "(x_1,y_1)=(-1,3)" and "(x_2,y_2)=(1,7)#

#rArrm=(7-3)/(1-(-1))=4/2=2#

#"use either of the 2 given points as a point on the line"#

#"using "(x_1,y_1)=(1,7)" then"#

#rArry-7=2(x-1)larrcolor(red)"in point-slope form"#

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