Point-slope form: a line from one point and its slope

0:00A line passes through the point three, five with slope negative two. What is its equation?

0:07Slope is the change in y for each step of one in x. Negative two means right one, down two.

0:16Point-slope form is y minus y one equals m times, x minus x one, where m is the slope and x one, y one is a point on the line.

0:28Put in m equals negative two and the point three, five: y minus five equals negative two times, x minus three.

0:38Watch the signs: we subtract the point, so it is minus three and minus five. Writing plus is a common mistake.

0:47To check, expand: negative two times x is negative two x, and negative two times negative three is six.

0:56Add five to both sides: y equals negative two x plus eleven.

1:03At x equals three: negative two times three is negative six, plus eleven is five. It fits.

1:12Now a line through two points: one, four and five, negative four.

1:18Run is the change in x: five minus one is four. Rise is the change in y: negative four minus four is negative eight.

1:28Slope is rise divided by run: negative eight divided by four is negative two.

1:35Use the slope with either point. With one, four: y minus four equals negative two times, x minus one.

1:45Check the other point, five, negative four: the left side is negative eight, and so is the right side.

1:54One point and the slope give the line: y minus y one equals m times, x minus x one.