Question

What equation in slope-intercept form represents the line that passes through the points

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 (2, -1), 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 - (- 1)) ÷ ((-3) - 2)  

                                         =   - 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 - (-1) =  - 1 (x - 2)

                                        y + 1 = - (x - 2)

we could also transform this into the slope-intercept form ( y = mx + c) by making y the subject of the equation:  

                                   since  y + 1 = - (x - 2)                                                    

                                                ∴  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.