The intercepts of an equation are given by the points where the graph touches one of the axes. This occurs whenever \( y=0 \) or \( x = 0\). For a given linear equation, we can find the intercepts very easily.
Considering \( y = 2x + 6 \), we have the following intercepts:
When \( x = 0 \), we have \( y = 2(0) + 6 = 6 \), so \( (0,6) \) is the y-intercept.
When \( y = 0 \), we have \( 0 = 2x + 6 \implies x = -3 \), so \( (-3,0) \) is the x-intercept.