Question

Think y=mx+b

Which graph represents the equation 12 = 3x+ 4y? Explain how you know.
Graph A
Graph B
Graph C

Answer 1

Explanation:

3x%2B4y=12 Start with the given equation

4y=12-3x Subtract 3+x from both sides

4y=-3x%2B12 Rearrange the equation

y=%28-3x%2B12%29%2F%284%29 Divide both sides by 4

y=%28-3%2F4%29x%2B%2812%29%2F%284%29 Break up the fraction

y=%28-3%2F4%29x%2B3 Reduce

Looking at y=-%283%2F4%29x%2B3 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-3%2F4 and the y-intercept is b=3

Since b=3 this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point

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

slope=rise%2Frun

Also, because the slope is -3%2F4, this means:

rise%2Frun=-3%2F4

which shows us that the rise is -3 and the run is 4. This means that to go from point to point, we can go down 3 and over 4

So starting at , go down 3 units

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

Now draw a line through these points to graph y=-%283%2F4%29x%2B3

So this is the graph of y=-%283%2F4%29x%2B3 through the points and