Question 225082
graph the line containing the given pair of points and find the slope. (-4,2), (1,-3)


Using the slope formula, or {{{(y[2] - y[1])/(x[2] - x[1])}}}, we can determine the slope, or m


m  =  {{{(y[2] - y[1])/(x[2] - x[1])}}}, with {{{y[2]}}} = - 3, {{{y[1]}}} = 2, {{{x[2]}}} = 1, and {{{x[1]}}} = - 4.


slope, or m  =  {{{(- 3 - 2)/(1 - - 4)}}} = {{{(- 5)/5}}} = {{{highlight_green(-1)}}} 


With a slope, or m of {{{- 1}}}, and one of its points, (1, - 3), we can use the point-slope formula, {{{y - y[1] = m(x - x[1])}}} to find the equation to graph the line.


{{{y - y[1] = m(x - x[1])}}} -------> {{{y - - 3 = m(x - 1)}}} ------> {{{y + 3 = - 1(x - 1)}}} ------> {{{y + 3 = - x + 1}}} ------> {{{y = - x - 2}}}. The graph of this linear equation is shown below.


{{{ graph( 300, 200, -6, 5, -6, 6, -x-2) }}}


You could also easily plot the 2 points, (- 4, 2) and (1, - 3) and join the points to get the linear graph. These 2 points can also be seen on the above graph, along with a y-intercept of - 2.


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