Is the line through (4, 6) and (1, 2) parallel to another line?

To determine whether the line through the points (4, 6) and (1, 2) is parallel to another line, we first need to calculate the slope of the given line.

The slope (m) of a line through two points (x₁, y₁) and (x₂, y₂) is calculated using the formula:

m = (y₂ – y₁) / (x₂ – x₁)

Let’s apply this formula to our points (4, 6) and (1, 2):

m = (2 – 6) / (1 – 4) = (-4) / (-3) = 4/3

Now that we have the slope of the line through the points (4, 6) and (1, 2), which is 4/3, we need to check if this slope is equal to the slope of the second line to confirm if they are parallel.

For two lines to be parallel, they must have the same slope. If you have another line in question, you can calculate its slope using the same method and compare.

In summary, to find out if the line through (4, 6) and (1, 2) is parallel to another line, compare the slope 4/3 with the slope of the other line. If they are the same, then yes, the lines are parallel.