Question

Given two linear equations, explain how you can determine if the lines are parallel without graphing them.

Answer 1

If two lines are parallel, their slopes will be the same. The slope is represented by the m in y=mx+b

Answer 2

For example, if you had
y=2x+5
and
y=2x+9
These would be parallel because they have the same number in front of the x.

But if you had
y=4x+3
and
y=7x+65
They would NOT be parallel because the number in front of the x is different.
Keep in mind that to determine if they are parallel your y has to be alone, no numbers in front, so if you had
5y=5x+10
and
y=x+8
they WOULD be parallel, because if you divided the first one by 5 to make the y single, you get y=x+2

Answer 3

A line passes through the point (–3, –4) and its y-intercept is (0, –9). What is the equation of the line that is parallel to the first line and passes through the point (3, –7)?