How do you find the point-slope form of the equation of the line passing through the points (-7, 0) and (5, 4)?

2 Answers
Jun 14, 2018

#y-4=1/3(x-5)#

Explanation:

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

#•color(white)(x)y-b=m(x-a)#

#"where m is the slope and "(a,b)" 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)=(-7,0)" and "(x_2,y_2)=(5,4)#

#m=(4-0)/(5-(-7))=4/12=1/3#

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

#"using "(5,4)" then"#

#y-4=1/3(x-5)larrcolor(red)"in point-slope form"#

Jun 14, 2018

#(y-4) = 1/3(x-5)#

Explanation:

First you determine the slope:

#(color(blue)(x_1),color(blue)(y_1)) = (-7,0)#

#(color(red)(x_2),color(red)(y_2))=(5,4)#

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

#color(green)m =(color(red)(4)-color(blue)(0))/(color(red)(5)-color(blue)((-7)))=4/12=1/3#

Now use the Point Slope form of a line:

You can use any point on the line, let's use the second one since both values are positive:

#(y-color(blue)(y_1)) = color(green)m(x-color(blue)(x_1))#

#(y-color(blue)(4)) = color(green)(1/3)(x-color(blue)(5))#