Question

Write the equation of a line in slope-intercept form that passes through the given points.

through: (0, 2) and (-4,1)

Answer 1

y = 0.25x + 2

Explanation:

`\bold{slope\, (m)=(change\ in\ Y)/(change\ in\ X)=(y_2-y_1)/(x_2-x_1)}`

(0, 2) ⇒ x₁ = 0, y₁ = 2

(-4, 1) ⇒ x₂ = -4, y₂ = 1

So the slope:

`\bold{m=(1-2)/(-4-0)=(-1)/(-4)=0.25}`

The point-slope form of the equation of the line passing through point (x₀,y₀) and with slope m is: y - y₀ = m(x - x₀)

m = 0.25

(0, 2) ⇒ x₀ = 0, y₀ = 2

Therefore:

y - 2 = 0.25(x - 0)

y - 2 = 0.25x {add 2 to both sides}

y = 0.5x + 2 ← the slope-intercept form of the equation