Question

How do you write an equation in point slope and slope intercept form given (1, 2) and (2, 5)?

Answer 1

`y-2=3(x-1)" and "y=3x-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)=(1.2)" and "(x_2,y_2)=(2,5)`

`m=(5-2)/(2-1)=3`

`"using "m=3" and "(x_1,y_1)=(1,2)" then"`

`y-2=3(x-1)larrcolor(red)"in point-slope form"`

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

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`"distributing and rearranging gives"`

`y-2=3x-3`

`y=3x-1larrcolor(red)"in slope-intercept form"`