Question

Write in slope-intercept form an equation of the line that passes through the points (−4, 2) and (6,−3).

Answer 1

Answer:

        y = -0.5x

Step-by-step explanation:

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

(−4, 2)    ⇒     x₁ = −4,  y₁ = 2

(6,−3)     ⇒     x₂ = 6,  y₂ = −3

So the slope:

$\bold{m=\dfrac{-3-2}{6+4}=\dfrac{-5}{10}=-0.5}$

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 = -0.5

(−4, 2)    ⇒     x₀ = −4,  y₀ = 2

Therefore:

               y - 2 = -0.5(x - (-4))

               y - 2 = -0.5x - 2               {add 2 to both sides}

               y = -0.5x          ←  the slope-intercept form of the equation (b=0)