Exercises: Graphing and Connecting Representations

Set $y = 0$, since you are solving for the $y$-intercept of the line.

Set both $x = 0$ and $y = 0$, then solve the resulting system of equations.

Set $x = 0$, since every point on the $y$-axis has $x$-coordinate zero.

Set $x = 1$, since the intercept lies one step across from the origin.

Up 3 and right 1, arriving at the point $(1, 8)$.

Right 3 and down 1, arriving at the point $(3, 4)$.

Down 3 and right 1, arriving at $(1, 2)$.

Down 3 and left 1, arriving at the point $(-1, 2)$.

Yes -- substituting gives 12, so the point satisfies the equation exactly.

Yes -- the point appears to sit on the line when the equation is graphed.

It cannot be determined without first graphing the line on a fine grid.

No -- substituting gives 31, not 12.