SOLUTION: I need help graphing y + 5 = -3/4 (x-6).

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Question 390709: I need help graphing y + 5 = -3/4 (x-6).
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

y+%2B+5+=+-3%2F4+%28x-6%29.....multiply by 4
4y+%2B+5%2A4+=+-%283x%2F4%294+-6%2A4%29
4y+%2B+20+=+-3x+-24%29
4y+=+-3x+-24+-20%29
4y+=+-3x+-44+%29
standard form
3x+%2B4y+=+-+44+%29
graph:

Solved by pluggable solver: Graphing Linear Equations


3%2Ax%2B4%2Ay=-44Start with the given equation



4%2Ay=-44-3%2Ax Subtract 3%2Ax from both sides

y=%281%2F4%29%28-44-3%2Ax%29 Multiply both sides by 1%2F4

y=%281%2F4%29%28-44%29-%281%2F4%29%283%29x%29 Distribute 1%2F4

y=-44%2F4-%283%2F4%29x Multiply

y=%28-3%2F4%29%2Ax-44%2F4 Rearrange the terms

y=%28-3%2F4%29%2Ax-11 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-3%2F4 (the slope) and b=-11 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-8

y=%28-3%2F4%29%2A%28-8%29-11

y=24%2F4-11 Multiply

y=-20%2F4 Add

y=-5 Reduce

So here's one point (-8,-5)





Now lets find another point

Plug in x=-4

y=%28-3%2F4%29%2A%28-4%29-11

y=12%2F4-11 Multiply

y=-32%2F4 Add

y=-8 Reduce

So here's another point (-4,-8). Add this to our graph





Now draw a line through these points

So this is the graph of y=%28-3%2F4%29%2Ax-11 through the points (-8,-5) and (-4,-8)


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 down -3 units and to the right 4 units to get to the next point), the y-intercept is (0,-11)and the x-intercept is (-14.6666666666667,0) ,or (-44%2F3,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=-11 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,-11).


So we have one point (0,-11)






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,-11), we can go down 3 units


and to the right 4 units to get to our next point



Now draw a line through those points to graph y=%28-3%2F4%29%2Ax-11


So this is the graph of y=%28-3%2F4%29%2Ax-11 through the points (0,-11) and (4,-14)