What equation in slope-intercept form represents the line that passes through the points (-3, 4) and (2, -1)? Explain how you found the equation.

        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.

1/5^2 = 7.56/45

1 x=22.52

2: 65/39=604+39x

65x-39x=604

26x=604

x=604/26

×=23.23