Final answer:
After converting the equations x + 2y = 6 and 4x + 8y = 24 into slope-intercept form, we find that both have the same slope and y-intercept, indicating they are coincident, or the same line.
Step-by-step explanation:
To determine if the equations x + 2y = 6 and 4x + 8y = 24 are intersecting, parallel, or coincident, we can put them into slope-intercept form (y = mx + b) and compare their slopes (m) and y-intercepts (b).
For the equation x + 2y = 6, solving for y gives us:
y = -0.5x + 3. Here, the slope m = -0.5 and the y-intercept b = 3.
For the equation 4x + 8y = 24, solving for y gives us:
y = -0.5x + 3. Here, the slope m is also -0.5 and the y-intercept b is also 3.
Since both lines have the same slope and the same y-intercept, they lie on top of each other. Therefore, the equations are coincident, which means they are the same line and have infinite points in common.