Question 940692
In an Absolute Value problem, the line will turn at some point if values become negative.
In simple problems this often occurs where y=0 or x=0
We will first set y=0
{{{y=abs(-2x+6)}}}
0=-2x+6 Subtract 2x from both sides
2x=6 Divide both sides by 2
x=3, So one point on the graph will be (3,0)
Pick an x below 3, say 0, and solve the equation for y:
y=-2x+6
y=-2(0)+6
y=6, so the line crosses the y axis at 6 and goes to point (3,0)
Pick an x greater than 3, say 4, and solve again
y=-2x+6y=-2(4)+6
y=-8+6
y=-2 Since this is absolute value, we disregard the sign and plot point (4,2)
With these three points we can graph the equation from (0,6) to (3,0) to (4,2)
{{{ graph( 400,400, -6, 5, -10, 10,abs(-2x+6))  }}}