Question

What is an equation of the line that passes through the points (3, 4) and (-4,-3)?

Answer 1

Answer:   y =  x  + 1

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, (3, 4) and (-4,-3), 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)  

                                         =  (4 - (- 3)) ÷ (3 - (-4))  

                                         =   1  

Finding the Equation

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

                                 ⇒  y - (-3) =  1 (x - (-4))

                                         y + 3 =  (x + 4)

 

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

                                    since  y + 3 =  (x + 4)

                                             ⇒     y = x + 1

                                       

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