Question 268627


Looking at {{{y=4x-5}}} we can see that the equation is in slope-intercept form {{{y=mx+b}}} where the slope is {{{m=4}}} and the y-intercept is {{{b=-5}}} 



Since {{{b=-5}}} this tells us that the y-intercept is *[Tex \LARGE \left(0,-5\right)].Remember the y-intercept is the point where the graph intersects with the y-axis


So we have one point *[Tex \LARGE \left(0,-5\right)]


{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  blue(circle(0,-5,.1)),
  blue(circle(0,-5,.12)),
  blue(circle(0,-5,.15))
)}}}



Now since the slope is comprised of the "rise" over the "run" this means

{{{slope=rise/run}}}


Also, because the slope is {{{4}}}, this means:


{{{rise/run=4/1}}}



which shows us that the rise is 4 and the run is 1. This means that to go from point to point, we can go up 4  and over 1




So starting at *[Tex \LARGE \left(0,-5\right)], go up 4 units 

{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  blue(circle(0,-5,.1)),
  blue(circle(0,-5,.12)),
  blue(circle(0,-5,.15)),
  blue(arc(0,-5+(4/2),2,4,90,270))
)}}}


and to the right 1 unit to get to the next point *[Tex \LARGE \left(1,-1\right)]

{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  blue(circle(0,-5,.1)),
  blue(circle(0,-5,.12)),
  blue(circle(0,-5,.15)),
  blue(circle(1,-1,.15,1.5)),
  blue(circle(1,-1,.1,1.5)),
  blue(arc(0,-5+(4/2),2,4,90,270)),
  blue(arc((1/2),-1,1,2, 180,360))
)}}}



Now draw a line through these points to graph {{{y=4x-5}}}


{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  graph(500,500,-10,10,-10,10,4x-5),
  blue(circle(0,-5,.1)),
  blue(circle(0,-5,.12)),
  blue(circle(0,-5,.15)),
  blue(circle(1,-1,.15,1.5)),
  blue(circle(1,-1,.1,1.5)),
  blue(arc(0,-5+(4/2),2,4,90,270)),
  blue(arc((1/2),-1,1,2, 180,360))
)}}} So this is the graph of {{{y=4x-5}}} through the points *[Tex \LARGE \left(0,-5\right)] and *[Tex \LARGE \left(1,-1\right)]