https://www.gregmat.com/quizzes/quiz/im-overwhelmed-coordinate-geometry-progress-quiz-4 (Question 8)
I didn’t understand why you chose the second option - it says that it is less than 6 and not equal to so how does that make the second point valid when the LHS value came to be 6
Can you explain further what you mean?
How do I approach in selection between option B and D in this question?
Can this be solved using any other approach which isn’t substitution? If yes, how?
In the solution, why did we choose (2,0)?
The slope of B > -1.
The slope of D is < -1.
Yes but for this specific question, substitution is faster imo.
Use the point (0,0) and A&C can be instantly ruled out.
Combine this with the slope fact above and you get B.
(2,0) is on the boundary of the graph, ie, the dashed line passes through this point.
Greg used (2,0) because substituting it into the equation corresponding to B gives 6=6, confirming that B has the correct boundary line.
D gives 8=6, so its boundary cannot be the line shown.
Also note that each tick mark on the graph is 2 units- this further explains why Greg chose (2,0).
The +10s and -10s on the graph are on the 5th ticks.
Hi, I undertood the substitution part. Can explain further about the slope logic?
How do we compare the less than -1 and greater than -1 values, relate to the graph and arrive at B?
Red line has slope less than -1
Blue line has slope greater than -1
The potentially counterintuitive part of the explanation is the language “greater/less than -1”
Remember, a line with a slope of -0.75, for example, has a greater slope than a line with slope -1
Whereas a line with a slope of -1.33 has a smaller slope than a line with slope -1.
