Math 1 · Unit 3 · Lesson 3 · part 5 of 9
Match by elimination: which graph fits the equation?
On a test you will often see one equation and several small graphs, and you have to pick the one that fits.
Match by elimination: which graph fits the equation?
On a test you will often see one equation and several small graphs, and you have to pick the one that fits. Do not plug in points. Read what the equation forces the graph to do, cross out every graph that breaks a rule, and check the one that is left. It is the three questions run backward, and for a line it takes three looks at most.
- 1The sign of m: which way does it go?A negative m falls from left to right. A positive m climbs. An m of 0 is a flat line. Cross out every graph that goes the wrong way.
- 2b: where does it cross the y-axis?The line has to cross the y-axis at (0, b). Cross out any survivor that crosses somewhere else.
- 3The size of m: steep or gentle?If two are still standing, a large slope is steep and a small one is gentle. That breaks the tie.
Worked: y = −2x + 3 against four graphs
Graph A climbs and crosses at 3. Graph B falls and crosses at −3. Graph C falls steeply and crosses at 3. Graph D falls gently and crosses at 3.
Look 1, the sign: m = −2 is negative, so the line falls. Cross out A (it climbs).
Look 2, b: b = 3, so it crosses at (0, 3). Cross out B (crosses at −3).
Look 3, the size: a slope of size 2 is steep, down 2 for every 1 right. Cross out D (gentle). C is left. Check it: from (0, 3), down 2 and right 1 lands on the line. Yes.
Write the answer with the rules
The answer is not just a letter. Say what ruled out each wrong choice: A goes the wrong way (m is negative), B crosses in the wrong place (b is 3), D is too gentle (the size of m is 2). That sentence is the understanding.
Same habit later for the exponential family (grows or decays first, then the starting value) and the quadratic family (opens up or down first, then the y-intercept).