SOLUTION: Graph the following equation. y = 3/4x + 2

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Question 111914This question is from textbook Beginning Algebra
: Graph the following equation.
y = 3/4x + 2This question is from textbook Beginning Algebra

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Graphing Linear Equations
In order to graph y=%283%2F4%29%2Ax%2B2 we only need to plug in two points to draw the line

So lets plug in some points

Plug in x=-8

y=%283%2F4%29%2A%28-8%29%2B2

y=-24%2F4%2B2 Multiply

y=-16%2F4 Add

y=-4 Reduce

So here's one point (-8,-4)


drawing%28+600%2C+600%2C+-18%2C6%2C+-14%2C+9%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-8%2C-4%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-8%2C-4%2C+.1%2C+1.5+%29+%29%0D%0A++%29

Now lets find another point

Plug in x=-4

y=%283%2F4%29%2A%28-4%29%2B2

y=-12%2F4%2B2 Multiply

y=-4%2F4 Add

y=-1 Reduce

So here's another point (-4,-1). Add this to our graph


drawing%28+600%2C+600%2C+-18%2C6%2C+-14%2C+9%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-4%2C-1%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-4%2C-1%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-8%2C-4%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-8%2C-4%2C+.1%2C+1.5+%29+%29%0D%0A++%29


Now draw a line through these points

drawing%28+600%2C+600%2C+-18%2C6%2C+-14%2C+9%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-18-10%2C0.75%2A%28-18-10%29%2B2%2C6%2B10%2C0.75%2A%286%2B10%29%2B2%29%2C%0D%0A++++blue%28+circle%28+-4%2C-1%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-4%2C-1%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-8%2C-4%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-8%2C-4%2C+.1%2C+1.5+%29+%29%0D%0A++%29 So this is the graph of y=%283%2F4%29%2Ax%2B2 through the points (-8,-4) and (-4,-1)


So from the graph we can see that the slope is 3%2F4 (which tells us that in order to go from point to point we have to start at one point and go up 3 units and to the right 4 units to get to the next point) the y-intercept is (0,2)and the x-intercept is (-2.66666666666667,0) ,or (-8%2F3,0)


We could graph this equation another way. Since b=2 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,2).


So we have one point (0,2)


drawing%28+600%2C+600%2C+-10%2C14%2C+-8%2C+15%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++%0D%0A++++blue%28+circle%28+0%2C2%2C+0.16%29%29%2C%0D%0A++++blue%28+circle%28+0%2C2%2C+0.16-0.05%29+%29%0D%0A++%29


Now since the slope is 3%2F4, this means that in order to go from point to point we can use the slope to do so. So starting at (0,2), we can go up 3 units


drawing%28++600%2C+600%2C+-10%2C14%2C+-8%2C+15%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C2%2C+0.16%29%29%2C%0D%0A++++blue%28+circle%28+0%2C2%2C+0.16-0.05%29+%29%0D%0A++blue%28+arc%28+0%2C+2%2B%283%2F2%29%2C+2%2C+3%2C+90%2C+270+%29+%29%0D%0A++%0D%0A++%29
and to the right 4 units to get to our next point

drawing%28++600%2C+600%2C+-10%2C14%2C+-8%2C+15%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+4%2C5%2C+0.16%29%29%2C%0D%0A++++blue%28+circle%28+4%2C5%2C+0.16-0.05+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C2%2C+0.16%29%29%2C%0D%0A++++blue%28+circle%28+0%2C2%2C+0.16-0.05%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+2%2B%283%2F2%29%2C+2%2C+3%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%284%2F2%29%2C+5%2C+4%2C+2%2C+180%2C+360+%29+%29%0D%0A++%0D%0A++%29
Now draw a line through those points to graph y=%283%2F4%29%2Ax%2B2


drawing%28+600%2C+600%2C+-10%2C14%2C+-8%2C+15%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C0.75%2A%28-10-10%29%2B2%2C14%2B10%2C0.75%2A%2814%2B10%29%2B2%29%2C%0D%0A++++blue%28+circle%28+4%2C5%2C+0.16%29%29%2C%0D%0A++++blue%28+circle%28+4%2C5%2C+0.16-0.05+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C2%2C+0.16%29%29%2C%0D%0A++++blue%28+circle%28+0%2C2%2C+0.16-0.05%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+2%2B%283%2F2%29%2C+2%2C+3%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%284%2F2%29%2C+5%2C+4%2C+2%2C+180%2C+360+%29+%29%0D%0A++%29 So this is the graph of y=%283%2F4%29%2Ax%2B2 through the points (0,2) and (4,5)