Question

How do you write an equation in point slope and slope intercept form given (2,3) with x-intercept 4?

Answer 1

`y-3=-3/2(x-2)" and "y=-3/2x+6`

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)=(2,3)" and "(x_2,y_2)=(4,0)`

`rArrm=(0-3)/(4-2)=-3/2`

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

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

`"distribute and rearrange"`

`y-3=-3/2x+3`

`rArry=-3/2x+6larrcolor(red)"in slope-intercept form"`