Question

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

Answer 1

`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"`

Answer 2

`(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))`