What this lesson covers
- The parameter dial: turn the coefficient and watch the line miss the marked point
- Why one substituted point beats computing the slope
- The same lock handed to you as a table of values instead of a picture
- A practice item where all four choices are the output of a named slip
Questions worked in the video
- 0:17The graph of line l in the xy-plane is shown. The equation of l is y = kx + 6. What is the value of k?
- 1:30The table gives three values of x and their corresponding values of g(x) for the linear function g, defined by g(x) = cx + 20. What is the value of c?
- 2:18The graph of line m in the xy-plane is shown. The equation of m is y = kx + 8. What is the value of k?
Chapters
- 0:00You only need one point of it
- 0:17The graph, and four believable answers
- 0:38Turning the dial until the line lands
- 1:30Same lock, handed over as a table
- 2:18Your turn
- 3:00Three ways this goes wrong
- 3:21Recap
Lesson transcript
The narration of the video, word for word, under its chapter headings.
0:17The graph, and four believable answers
Here is a line on the grid, and its equation is y equals k x plus six. The k is missing. The graph marks the point four, three. Four choices, and three of them come from a real reading mistake.
0:38Turning the dial until the line lands
You do not need the whole line. You need one point it actually passes through. The graph marks four, three, so put those in. Three equals k times four, plus six. Now watch the dial. Turn it to negative four thirds, the flipped fraction, run over rise. The line swings under the point and lands two and a third below it. Wrong value, wrong line. Turn it to positive three fourths, and the line climbs instead of falling. At x equals four it reads nine, six above the point. Turn it to six, the number already sitting in the equation, and the line leaves the grid entirely. Only one setting lands on the point. Four k equals negative three, so k is negative three fourths. Check it: negative three, plus six, is three. B.
1:30Same lock, handed over as a table
Same job, different evidence. A table instead of a graph. g of x equals c x plus twenty, and the table gives three rows. None of them is x equals zero, so the twenty is not sitting in the table anywhere. It does not matter. Take any row that is actually there. Row one says x is three, g of x is eight. Substitute: eight equals three c plus twenty. Three c is negative twelve, so c is negative four. One row was enough. And if you use two rows instead, subtract the y values and the x values in the same order. Flip one of them and the dial lands on positive four, which sends row one to thirty two.
2:18Your turn
Your turn. The graph of y equals k x plus eight passes through the marked point six, negative one. Ten seconds. Substitute: negative one equals six k plus eight. Six k is negative nine, so k is negative three halves. A. Negative two thirds is the flipped fraction again. Two comes from putting the coordinates in backwards. And eight is the intercept, not the coefficient.
3:00Three ways this goes wrong
Three ways this goes wrong. Flipping the fraction and putting the run on top. Reading a line that falls as if it rises. And handing back the intercept when the question asked for the coefficient. All three die the moment you substitute a real point.
3:21Recap
Do not solve the line. Substitute one point.
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.