Question

What is the equation of the line that passes through the point (5, -2) and has a slope of 6/5

Answer 1

Answer:

        y + 2 = ⁶/₅(x - 5)     {the point-slope form of the equation}

        y = ⁶/₅x - 8            {the slope-intercept form of the equation}  

         6x - 5y = 40           {the standard form of the equation}

Step-by-step explanation:

The point-slope form of equation is: y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope.

m = ⁶/₅

(5, -2)    ⇒   x₀ = 5,  y₀ = -2

So, the point-slope form of the equation:

y + 2 = ⁶/₅(x - 5)

Therefore:

y + 2 =  ⁶/₅x - 6          {subtract 2 from both sides}

y = ⁶/₅x - 8              ←  the slope-intercept form of the equation

-⁶/₅x + y = - 8                    {multiply both sides by (-5)}

6x - 5y = 40               ←  the standard form of the equation