Question

A line passes through (−1, 7) and (2, 10).

Answer 1

The slope m of a line through points $A(x_1, y_1)$ and $B(x_2, y_2)$  is given by :

$\displaystyle{m = \frac{y_2-y_1}{x_2-x_1}$



Thus, the slope of the line passing through points (−1, 7) and (2, 10) is 

$\displaystyle{m= \frac{10-7}{2-(-1)}= \frac{3}{3}=1$


The equation of a line with slope m passing through a point P(a, b) is given by
                                        (y-b)=m(x-a).


We can consider any of the points (-1, 7), or (2, 10). Let's choose (2, 10):

                                        y-10=1(x-2)
                                        y-10=x-2
                                           y-x=-2+10
                                           y-x=8
                                       

  Answer: C. −x+y=8