Question

1. if the slope of the two equations you just entered into desmos is the same, why are there two different lines and not just one line?

because the slope of the lines is the same, but the b values are different, so they intersect the y - axis at different values
there are not two different lines. the fact that the slope is the same means the two lines are identical
because the slope of the lines is the same, therefore by a math rule, they have to be two different lines

Explanation:

The equation of a line in slope - intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. If two lines have the same slope (\(m\)) but different \(y\) - intercepts (\(b\) values), they are parallel lines (different lines). If two lines have the same slope and the same \(y\) - intercept, they are the same line.

Answer:

Because the slope of the lines is the same, but the 'b' values are different, so they intersect the y - axis at different values.