Open Middle®
Directions: List 2 points form a line that satisfies the following (you can use numbers 0-5, but you can only use a number once). Write the equation of the line represented by the points:
a) Its rate of change must be larger than 2
b) Its y-intercept must be smaller than 3
c) It must share a point with the line described by the rate of change and intercept from a) & b)
Write the equation of the line represented by the points:
Hint
What is the equation of the line described in a) and b)?
Answer
(0,2) and (1,5) are the points, y = 3x + 2 is the equation of the line formed by those two points
Source: Bryan Anderson
Not sure I understand the directions or the hint here. When it says “you can only use a number once,” I thought it meant all 6 numbers to fill in the blanks for (__,__), (___,___) and y = ___ x + ____ had to be unique. I tried to find that solution & convinced myself it doesn’t exist.
The answer re-uses the intercept from the equation, though, so I guess only the two points’ coordinates need to be unique, and you listed 3 points of which either of the 2 with unique coordinates could be the answer… right?
But if that’s the case, wouldn’t y = 3x + 0 and (2, 6) with either (1, 3) or (3, 9) also work? Or y = 3x + 1 and (0, 1) or (1, 4) with (2, 7)? Or y = 4x + 0 with (1, 4) and (2, 8)?
Or come to think of it, y = 1x + …
Writing the equation of the line was and end product, and I didn’t make that distinction in the directions- thanks. I shortened the interval to make two unique answers. The problem with your list of possible equations is that they do not share a common point with the line created by the parameters in A) and B). That line is y=2x + 3. I may have to look at re-wording the whole problem.
How does this sound?
List 2 points (__,__) and (__,__) on a line that satisfies the criteria described below in a) & b). You can use numbers 0-5, but you can only use each number once.
a) Its rate of change must be larger than 2
b) Its y-intercept must be smaller than 3
Write the equation of the line represented by the points:
y = __x +___