What this lesson covers
- The coefficient readout: two slots, both filled by looking, neither ever computed
- Why the picture beats the slope formula on a "which equation" item
- Standard form Ax + By = C read for direction, steepness and crossing without rearranging it
- A practice item where all four choices are the output of a named misreading
Questions worked in the video
- 0:15Line l is graphed in the xy-plane. Which equation could define line l?
- 1:32A line is graphed in the xy-plane. Which equation, in the form Ax + By = C, could define it?
- 2:26Line m is graphed in the xy-plane. Which equation could define line m?
Chapters
- 0:00Solve none of them
- 0:15A picture, and four equations
- 0:39Two slots, filled by looking
- 1:32Same read, standard form
- 2:26Your turn
- 3:08Three ways this goes wrong
- 3:27Recap
Lesson transcript
The narration of the video, word for word, under its chapter headings.
0:15A picture, and four equations
Here is the whole question. A line is graphed, and four equations are offered. Only one of them could have drawn that picture. Most students grab a point and start substituting. There is a faster way in. Two things about that line are readable without any algebra at all: which way it runs, and where it crosses. Those are the two slots.
0:39Two slots, filled by looking
Read the picture into two slots, and only two. Slot one is the slope. The line falls as you move right, so the slope is negative. And it is steeper than the dashed 45 degree guide, so its size is bigger than one. Slot two is the crossing. The line meets the y axis at four. Now let the slots do the killing. Choice C rises. The picture falls, so slot one throws it out. Choice D is shallower than the guide, so slot one takes that one too. Choice A crosses at three, and the picture crosses at four, so slot two ends it. One equation is left standing, and nothing was ever solved. That is the whole method. Fill two slots off the picture, then let each wrong equation break one of them. No substitution, no slope formula, no rearranging.
1:32Same read, standard form
Same read, harder costume. Now the choices arrive in standard form, Ax plus By equals C, and rearranging four of them is exactly the work we are trying to avoid. You do not have to rearrange anything. The signs of A and B give you the direction. Same signs, the line falls. Opposite signs, it rises. The size of A against the size of B gives you the steepness. Bigger A is steeper than the guide. And for the crossing, just ask whether the point the picture marks satisfies the equation. Three choices die on one slot each. Choice A has the same signs, so it falls, and the picture rises. Choice D has the bigger A, so it is steeper than the guide. Choice B fails the crossing test, landing at plus three instead of minus three. C is what is left.
2:26Your turn
Here is the graph, and here are the four equations. Both slots are readable straight off the picture. Your turn. Ten seconds. Fill both slots, then kill three. The line falls, and it is steeper than the guide, so the slope is negative and its size is bigger than one. It crosses below the origin, at negative five. Choice D rises. Choice C is too shallow. Choice A crosses at positive five. B is the only one both slots allow.
3:08Three ways this goes wrong
Three ways this goes wrong. Taking the sign from the direction your eye is travelling instead of the direction the line is travelling. Swapping the slope and the crossing between the two slots. And seeing a crossing below the origin and writing it down as positive.
3:27Recap
Two slots. Read, then reject.
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.