Answer
$x$-intercept: $(-3, 0)$
$y$-intercept: $(0, 6)$
Work Step by Step
This equation is in the slope-intercept form which is given by the equation:
$y = mx + b$
where $m$ is the slope and $b$ is the $y$-intercept.
The $y$-intercept is defined as the point on the graph when $x$ is $0$.
In the equation $y = 2x + 6$, the $y$-intercept is $6$; therefore, the $y$-intercept occurs at $(0, 6)$.
We can find the $x$-intercept by setting $y$ equal to $0$ because the definition of the $x$-intercept is that it is the point on the graph when $y$ is $0$.
Let us set $y$ equal to $0$ to find the $x$-intercept:
$0 = 2x + 6$
Subtract $6$ from each side of the equation to move constants to one side of the equation:
$-6=2x$
Divide both sides of the equation by $2$ to solve for $x$.
$ -3=x$
The $x$-intercept occurs at $(-3, 0)$, and the $y$-intercept occurs at $(0, 6)$.
