Question

find and plot the ( x )- and ( y )-intercepts of the following equation. then graph the equation based on those points.

( x - 2y = 6 )

the ( x )-intercept is \boxed{}.
(write the intercept as an ordered pair.)

the ( y )-intercept is \boxed{}.
(write the intercept as an ordered pair.)

plot the two intercepts in the plane below. then graph the equation passing through those intercepts.

coordinate plane with x-axis from -10 to 6 and y-axis from -8 to 10, grid lines visible

Explanation:

Step1: Find x-intercept, set $y=0$

Substitute $y=0$ into $x-2y=6$:
$x - 2(0) = 6$
$x = 6$
So the x-intercept is $(6, 0)$.

Step2: Find y-intercept, set $x=0$

Substitute $x=0$ into $x-2y=6$:
$0 - 2y = 6$
$-2y = 6$
$y = \frac{6}{-2} = -3$
So the y-intercept is $(0, -3)$.

Step3: Graph the line

Plot the points $(6, 0)$ and $(0, -3)$ on the coordinate plane, then draw a straight line passing through both points.

Answer:

The x-intercept is $(6, 0)$
The y-intercept is $(0, -3)$

(For the graph: Mark the point $(6,0)$ on the positive x-axis, mark $(0,-3)$ on the negative y-axis, then connect these two points with a straight line extending beyond both points.)