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graph y = –2x + 1 and y =1/2 x + 6

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When you graph equations like this you use the Y= m x + b format. Both of those equations are already in that format.

So you start with "b" always it's our starting position. For equation A it's 1 and equation B it's 6.  This tells us where to start on the y-axis--b represents the y-intercept. Make a point at the y-intercept: Equation A (0,1) Equation B (0,6)

Next the "M" represents how we move from the first point."M" represents rise (how many you move up/down) over run (how many you move left/right). If there's a negative sign associate it with the RISE. Positive number move up and to the right. Negative numbers move down and to the left on the x & Y axis.  if it's a whole number always imagine it's over the number 1 it will make it easy for you. for example -2 think of it as -2/1.

Equation A

from (0,1) you move down 2  and over to the right 1 because m = -2 or -2/1. The next point will be (1, -1). Draw a line thru the points with a ruler.

Equation B

from (0,6) you move up 1 and over 2 because m = 1/2. The next point will be (1, 8). Draw a line thru those two points.