Write the number rule for these order pairs p6. (1,4),(2,7),(3,10),(4,13). rule
x = + 1
y = + 3
slope is the same for all line segments
= 3
so y = 3x + b
plug in one of the points, I will use (1,4)
4 = 3(1) + b
b = 1
rule, or the equation is
y = 3x + 1
To find the number rule for the given ordered pairs, let's examine the pattern in the y-values.
In this case, notice that as the x-values increase by 1, the y-values increase by 3.
For example:
1. (1, 4) to (2, 7) - increase in x by 1, increase in y by 3.
2. (2, 7) to (3, 10) - increase in x by 1, increase in y by 3.
3. (3, 10) to (4, 13) - increase in x by 1, increase in y by 3.
Based on this pattern, we can determine the number rule:
For every increase in x by 1, the y-value increases by 3.
Therefore, the number rule for these ordered pairs is:
y = 3x + b
To find the value of b (y-intercept), we can substitute the coordinates of any of the points into the equation and solve for b.
Let's use the first point (1, 4) to find b:
4 = 3(1) + b
4 = 3 + b
Subtracting 3 from both sides:
1 = b
So, the final number rule for these ordered pairs is:
y = 3x + 1