Answer: Try to figure it out first. If you can't, then you haven't learned the material and you won't be able to understand subsequent lessons.
Step-by-step explanation:
Question 1 checks that you know several things:
● Point (5,8) means x=5 and y=8.
● Which number is the y intercept in equation y = m x + b.
m is NOT the y intercept.
b IS the y intercept.
Guess which is the slope...
● The y intercept is value of y when x is zero. But m times zero is zero, no matter what m is, so m can't be the y intercept. On the other hand, m x + b evaluates to b when x is zero.
● The meaning of an inequality and how it is graphed:
A solid line means the line is included in the graph (≤ or ≥).
A dotted line means the line is not included (< or >).
The shaded area indicates points in that area are in the solution set of the inequality.
● To see if point (A,B) is in the solution set, substitute A for x and B for y, and see if the result is true.
Say (A,B) = (5,6), and the statement is y < 2x + 3. You substitute A (5) for x and evaluate the right hand side to a number (13), and substitute B (6) for y on the left hand side to give a statement about two numbers: 6 < 13. If the statement is true, then (A,B) is in the solution set.
Then the region containing (A,B) will be shaded (inequality), or a solid line (equation).
Question 2 tries to see if you realize you can't draw a line between two points without first plotting both points.
Question 3 checks to see if you know how to tell if an equation matches a line on graph paper. You can look at the line, find the y intercept (b) and the slope (m), and look for an equation y = m x + b.
For instance, the red line crosses the y axis at (0,4), x = 0 (always true for a y intercept), and y = 4. So the equation for the red line must be
y = m x + 4. If you substitute (0,4), you get 4 = m × 0 + 4 = 4, a true statement.
You can figure the slope of the red line as m = rise/run. The answer is m=2, so the equation is y = 2x+4.
Or you can just check all of the choices. Takes longer but you don't have to know how to find slope.
But after doing this (or even without doing it), you check to see if a few points from the line make the equation true. The red line includes (-4,-4). So check -4 = 2(-4) + 4. Since -8+4 is -4, the result is true. Also check (0,4) and (-2,0) because they are easy to do. 4 = 2(0)+4, true, and 0 = 2(-2) + 4, true. y = 2x + 4 is the equation of the red line.
If the check fails, then either you don't know how to read the slope and y intercept, or else you don't know how to substitute x and y into the equation.
Another way to eliminate incorrect choices quickly is to substitute (-3,-2), x = -3, y = -2, into each pair. If either equation evaluates to false, eliminate that choice. But that might not eliminate all but one choice, so you need to test all of them.
The last question checks to see if you can figure out which axis is x and which is y, and if you know (-3,-2) means x=-3, y=-2, and not x=-2, y=-3.
