color(brown)("It does not matter if you have "x=2y+2" or by ")It does not matter if you have x=2y+2 or by
color(brown)("manipulation "y=x/2-1 ". They both plot the same ")manipulation y=x2−1. They both plot the same color(brown)("straight line.")straight line.
So the slope color(blue)("(gradient) is 2")(gradient) is 2. That is: for every 1 along you go up 2. You always read from left to right for the gradient.
+2 means the line goes up whilst -2 means it goes down!
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color(blue)("To determine "x_("intercept"))To determine xintercept
The line will cross the x-axis at y=0
Set y=0 giving:
x=2(0)+2x=2(0)+2
color(blue)(x_("intercept")=2)xintercept=2
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color(blue)("To determine "y_("intercept"))To determine yintercept
The line will cross the y-axis at x=0
Set x=0 giving:
0=2y+20=2y+2
Subtract color(red)( 2)2 from both sides
0color(red)(-2)=2y+2color(red)(-2)0−2=2y+2−2
-2=2y+0−2=2y+0
Divide both sides by color(red)(2)2
-2/(color(red)(2))=2/(color(red)(2)) xx y−22=22×y
But 2/(-2)=-1" and "2/2=+12−2=−1 and 22=+1
-1=1xxy−1=1×y
color(blue)(y_("intercept")=-1)yintercept=−1
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![Tony B]()
