Question

Write an equation in slope intercept form of the line that passes through (-2,10) and (1,1).

Answer 1

y = -3x + 4

Explanation:

The slope of a line passing through two points: (x₂, y₂) and (x₁, y₁) is:

`\bold{m=(y_2-y_1)/(x_2-x_1)}`

(-2, 10) ⇒ x₁ = -2, y₁ = 10

(1, 1) ⇒ x₂ = 1, y₂ = 1

So:

`\bold{m=(1-10)/(1+2)=(-9)/(3)=-3}`

The point-slope form of equation of line is y - y₀ = m(x - x₀)

We can pick any of given poins, so:

x₀ = 1, y₀ = 1 and m = -3

y - 1 = -3(x - 1)

y = -3x + 3 + 1

y = -3x + 4 ← slope intercept form of the line

Answer 2

(-2,10)=x1,y1

(1,1)=x2,y2

we have,

(y-y1)=(y2-y1)/(x2,x1)[(x-x1)]

(y-10)=(1-10)/(1+2)[x+2]

y-10=-9/3(x+2)

y-10=-3(x+2)

y-10=3x+6

y=3x+16