Question

How do you write the point slope form of the equation given (0,0) and (-3,-2)?

Answer 1

`y+2=2/3(x+3)`

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

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

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

`y-(-2)=2/3(x-(-3))`

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