Finding points on a line when given an equation
About this video
Line K is written as (y - 6)/(x - 5) = 4/3, which says the slope between any point (x, y) on the line and (5, 6) is 4/3. The video tests four points by substituting their x and y values and checking whether the result simplifies to 4/3, finding that (14, 18) and (2, 2) lie on the line.
You'll be able to
- explain that (y - 6)/(x - 5) = 4/3 means the slope from (5, 6) to any point on the line is 4/3.
- substitute a point into a line's equation to decide whether it lies on the line.
- simplify fractions, including negative over negative, when checking a slope.
Key words
- slope
- The change in y divided by the change in x between two points on a line.
- substitute
- Replace a letter in an equation with a number to see if the equation is true.
Transcript
- [Instructor] We can write the equation of line K as Y minus six over X minus five is equal to four thirds. Which of the following points lie on line K? Choose all answers that apply, so pause this video, have a go at this before we do this together. Okay, so when we just look at this equation here, they're saying that the slope of the line between any arbitrary X, Y and the coordinate five, comma, six is four thirds, and if you manipulate it, you could put it into other forms, like Y equals MX plus B or slope intercept form or standard form, but we actually don't have to know any of that to solve this problem.
To solve this problem, we really just have to substitute our Xs and Ys into this equation to see if it's true, so in this first one right over here, X is eight, Y is 11, so I have 11 minus six over eight minus five, so this is equal to five over three, not four over three, so I'd rule that out.
Another way to think about it, we just calculated the slope of the line between this point and the point 5, comma, six, and we see that it is not four, three. All right, this next one, we'll do the same idea. The Y is 20 minus six over the X, 16 minus five. This is equal to 14 over 11, not four over three.
Rule that one out. Let's do this one. 18 minus six over 14 minus five. This is equal to 12 over nine, and both the numerator and the denominator are divisible by three, which gets you four over three. Yes, this one is good, and last but not least, when Y is two, two minus two minus six over two minus five is equal to negative four over negative three, which is also equal to positive four over three, so we like that one as well.
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