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

2 Answers
Mar 3, 2018

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"

Mar 3, 2018

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!