Question

A line passes through the points (3,0) and (4,2). What is its equation in slope-intercept form?

Answer 1

Answer:

y = 2x - 6

Step-by-step explanation:

Slope intercept form:

     Equation of the line:

            $\sf \boxed{ y = mx +b}$

      Here m is the slope and b is the y-intercept.

Step 1:  Find the slope

       (3 , 0) ⇒ x₁ = 3  & y₁ = 0

       (4 , 2) ⇒ x₂ = 4  &  y₂ = 2

      $\sf \boxed{Slope=\dfrac{y_2-y_1}{x_2-x_1}}$

                $\sf = \dfrac{2 -0}{4-3}\\\\= \dfrac{2}{1}\\\\=2$

     m = 2

Step2: Now, substitute the value of 'm' in the equation.

    y = 2x + b

Step3: In the above equation plug in any point. Here, (3 ,0) is chosed.

      0 = 2*3 + b

      0 = 6 + b

      -6 = b

     b = -6

Step4: Equation of the line:

          y = 2x - 6