Final answer:
The x-intercept of the equation 2x-6y=-12 is (-6, 0), and the y-intercept is (0, 2). We solve separately for each intercept by substituting zero in for the variable not being calculated.
Step-by-step explanation:
The question asks for the x-intercept and y-intercept of the linear equation 2x-6y=-12 as ordered pairs. To find the x-intercept, we set y to 0 in the equation and solve for x. For the y-intercept, we set x to 0 and solve for y.
To find the x-intercept:
- Set y to 0 in the equation: 2x - 6(0) = -12.
- Solve for x: 2x = -12 ⇒ x = -6.
- The x-intercept is (-6, 0).
To find the y-intercept:
- Set x to 0 in the equation: 2(0) - 6y = -12.
- Solve for y: -6y = -12 ⇒ y = 2.
- The y-intercept is (0, 2).
The linear equation y = mx + b is also mentioned where b represents the y-intercept and m represents the slope. In this context, by rearranging the original equation, we get y = ⅓x + 2, from which we can confirm the calculated y-intercept is 2 when x is zero.