Question

How do you write an equation in point-slope form of the line that passes through the given points (-1,-8),(4,-6)?

Answer 1

`y+8=2/5(x+1)`

Explanation:

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

`color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))`

`"where m is the slope and "(x_1,y_1)" a point on the line"`

`"calculate m using the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(-1,-8)" and "(x_2,y_2)=(4,-6)`

`rArrm=(-6-(-8))/(4-(-1))=2/5`

`"using "m=2/5" and "(x_1,y_1)=(-1,-8)`

`y-(-8)=2/5(x-(-1))`

`rArry+8=2/5(x+1)larrcolor(red)"in point-slope form"`

Answer 2

`y+6=-0.4(x-4)`

Explanation:

Hey!

Well firstly, we know the point-slope form equation:

`y−b=m(x−a)`

Next, we need to input the values that we are given in the question, in this case (-1,-8), (4,-6). To start, let's solve for m, or slope.

`m=(Δy)/(Δx)`

Inputting variables:

`m=[(-8)-(-6)]/[(-1)-(4)]=(2)/(5)=-0.4`

Finally, we input the slope value and one of the given points for the `b` and `a` values.

`y+6=-0.4(x-4)`

Good luck!