Respuesta :

Answer:   y - 12 = 5 (x - 4)    OR   y = 5x - 8

Step-by-step explanation:

For us to write the equation for this line, we need to (1) find the slope of the line, and (2) use one of the points to write an equation:

The question gives us two points, (4​,12​) and ​(−1​,−13​), from which we can find the slope and later the equation of the line.

Finding the Slope  

The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)  

                                          =  (12 - (- 13)) ÷ (4 - (- 1))

                                          =   25  ÷  5

                                         =  5

 

Finding the Equation

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line; where (x₁ , y₁) = (4, 12):

                        ⇒  y - 12 = 5 (x - 4)

    we could also transform this into the slope-intercept form ( y = mx + c)

                   since y - 12 = 5 (x - 4)

                              y - 12 =  5x + 5 (-4)

                                    y = 5x - 20 + 12

                          ⇒  y = 5x - 8

To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.

Ver imagen JoshEast
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