Final answer:
To find three additional points through which the given line passes, use the point (4, 2) and the slope m of the line. The correct answer is b. (3, 6), (2, 8), (1, 10).
Step-by-step explanation:
To find three additional points through which the line passes, we can use the given point (4, 2) and the slope of the line. Let's use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
1. Substitute the given point into the equation to find b. We have 2 = m * 4 + b.
2. Now that we have the values of m and b, we can substitute them into the equation to find the y-values for the three additional points. For example, if we choose (6, 3), we substitute 6 for x and solve for y: y = mx + b = m * 6 + b.
The process of addition follows these basic rules:
Commutative property: Changing the order of addends doesn't change the sum. For example:
5
+
3
=
3
+
5
=
8
5+3=3+5=8.
Associative property: Changing the grouping of numbers being added doesn't change the sum. For example:
(
2
+
3
)
+
4
=
2
+
(
3
+
4
)
=
9
(2+3)+4=2+(3+4)=9.
Identity property: Adding zero to any number doesn't change the value of the number. For example:
5
+
0
=
5
5+0=5.
Inverse property: The sum of a number and its additive inverse (negative counterpart) is always zero. For example:
5
+
(
−
5
)
=
0
5+(−5)=0.