Question

write the equation of a line that passes through the points (−3, 5) and (2, 10) in slope-intercept form

Answer 1

Slope-intercept form         y = mx + b

                          where    m------> slope

                                         b-------> y-intercept

                                        m= (y1-y2)/(x1-x2)

                                        P1(-3,5)      (x1,y1)

                                        P2(2,10)      (x2,y2)

                                         m= (5-10)/(-3-2)

                                         m= (-5)/(-5)

                                         m=1

               Until now, the equation is y=mx+b

                                                        y=1.x+b

                                                        y=x+b

But, whe can plug  the point   P2(2,10) in y =x+b

                                                     10 =2 + b

                                                   10 - 2 = b

                                                           b= 8

Then, the equation is              y=mx+b

                                                y= x+8   <-------------------Solution

Verification                    P1(-3,5)       y = x+8        5=-3+8     Ok

                                      P2(2,10)      y = x +8      10 = 2+8   Ok