Question

On the same coordinate planes, mark all points such that y=x+3, y=-x+3, y=|x|+3

Answer 1

To mark these points, we can use the coordinate plane and plot the points where each equation intersects the x-axis and y-axis.

For y=x+3, when x=0, y=3. When y=0, x=-3. So, we can plot the point (0,3) and (-3,0).

For y=-x+3, when x=0, y=3. When y=0, x=3. So, we can plot the point (0,3) and (3,0).

For y=|x|+3, we can break this equation into two separate equations:

When x is positive, y=x+3. When x=0, y=3. When y=0, x=-3. We can plot the point (0,3) and (-3,0).

When x is negative, y=-x+3. When x=0, y=3. When y=0, x=3. We can plot the point (0,3) and (3,0).

So, the three points where all three equations intersect are (0,3), (-3,0), and (3,0).