What this lesson covers
- The rise-run stair: signed run, signed rise, slope read off the picture
- Two slips shown happening: run over rise, and subtracting in opposite orders
- Point-slope as the fast lane, checked against the other point
- Converting to y = mx + b, and why a point's y-value is never the intercept
Questions worked in the video
- 0:17A line passes through (-3, 7) and (6, 1). Which equation defines the line?
- 2:29A line passes through (2, -3) and (6, 3). Which equation defines the line?
Chapters
- 0:00Draw the stair
- 0:17Two points, four believable equations
- 0:37The stair, the slope, and two slips
- 1:47Point-slope into y = mx + b
- 2:29Your turn
- 3:10Three ways this goes wrong
- 3:29Recap
Lesson transcript
The narration of the video, word for word, under its chapter headings.
0:17Two points, four believable equations
A line passes through the points negative three, seven and six, one. Which equation defines that line? Four choices. Three of them are exactly what you get from one specific slip, and every one of those slips has a name.
0:37The stair, the slope, and two slips
Do not reach for the formula. Draw the stair. Plot both points, go across from the first one to the second, then go up or down to land on it. Across nine. Down six. That is your run and your rise, read straight off the picture. The rise goes on top. Negative six over nine, which reduces to negative two thirds. Now watch two slips happen. Put the run on top instead, and you get nine over negative six, which is negative three halves. Anchor that and you land on choice A. Or subtract in opposite orders. Seven minus one on top, six minus negative three on the bottom, and the sign flips to positive two thirds. That is choice D. Same two points, three different slopes. With the slope in hand, point slope form is the fast lane. y minus one equals negative two thirds, times the quantity x minus six. The y and the x come straight off the point you used. Now test the other point. Negative three minus six is negative nine. Negative two thirds of negative nine is six. One plus six is seven. That is the other point exactly. The line is right.
1:47Point-slope into y = mx + b
The choices are written in y equals m x plus b form, so finish the conversion. Distribute the negative two thirds. You get negative two thirds x, plus four. Then add the one across. y equals negative two thirds x, plus five. Five is where the line crosses the y axis. Neither point you were given has x equal to zero, so neither seven nor one could ever be the intercept. That is choice C, dead. And if you had anchored on the other point instead, y minus seven equals negative two thirds times the quantity x plus three, you get the same line. Either point works.
2:29Your turn
Your turn. A line passes through two, negative three and six, three. Which equation defines it? Ten seconds. Across four, up six. Rise over run is six over four, which is three halves. Anchor on six, three. Three equals three halves times six, plus b, so b is negative six. y equals three halves x minus six. That is choice C. Check it against two, negative three. Three minus six is negative three. It holds.
3:10Three ways this goes wrong
Three ways this goes wrong. Run over rise instead of rise over run. Subtracting in one order on top and the other order on the bottom. And grabbing a y value from one of the points and calling it the intercept. Draw the stair, keep the order, and substitute back.
3:29Recap
Two points, one stair, one equation.
Read the written version: the Linear equations · two variables strategy guide, then try 25 hard Linear equations · two variables questions with full explanations. Both are free, no account needed.