Coordinates and plotting a relationship

Write a point as \((x,y)\): move horizontally by \(x\), then vertically by \(y\). The axes meet at \(O(0,0)\). Every point on the \(x\)-axis has \(y=0\); every point on the \(y\)-axis has \(x=0\). A graph represents pairs of values satisfying a relationship.

Example

For \(y=2x+1\), calculate several pairs, plot them using the axis scales and draw the straight line through them. A third point checks the first two.

Do not exchange the coordinates: \((2,5)\) and \((5,2)\) usually represent different points.