Question

The line passes through the point (3,12) and has the same slope as the line y = 5x - 7.

Answer 1

Answer:

           y - 12 = 5(x - 3)    {the point-slope form of the equation}

            y = 5x + 9            {the slope-intercept form of the equation}

           5x - y = -9            {standard form of the equation}

Step-by-step explanation:

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

y = 5x - 7     ⇒   m = 5

(3, 12)    ⇒   x₀ = 3,  y₀ = 12

So, the point-slope form of the equation:

y - 12 = 5(x - 3)

Therefore:

y - 12 = 5x - 3         {add 12 to both sides}

y = 5x + 9             ←  the slope-intercept form of the equation

y = 5x + 9               {subtract5x from both sides}

y - 5x = 9               {multiply both sides by (-1)}

5x - y = -9             ← the standard form of the equation