Equations in standard form

Question

Find an equation of the line passing through the pair of points (-3,-7) and (-4,-8). Write the equation in standard form (Ax+By=C)

Answer 1

When you know 2 points you can find the slope.     (y₂ - y₁)/(x₂ - x₁) = m

 

     (-8 - (-7))/((-4 - (-3)) = (-8 + 7)/(-4 + 3) = -1/-1 = 1      the slope is 1.

 

since we have a point, either (-3,-7) or (-4,-8) and a slope = 1

 

Now use point-slope form of the equation   →   y - y₁ = m(x - x₁) 

 

Lets use the point (-3,-7) and slope m = 1

 

Equation   →    y - (-7) = 1(x - (-3))

 

                          y + 7 = x + 3       To get this into standard form we subtract 7 from both sides

 

                              -7         -7

 

                                y =  x - 4         Now subtract x from both sides

 

                               -x = -x - 4  

 

                          -x + y = -4            

 

If you want the coefficient of x to be positive you could multiply everything by -1 and get

 

                            x - y = 4

 

CHECK  →  plug both given points into this equation to make sure they both work.

 

                           -3 - (-7) = 4                      -4 - (-8) = 4

                              -3 + 7 = 4                         -4 + 8 = 4

                                     4 = 4   √                            4 = 4   √