Question

Write a rule and an equation to fit the pattern in the table. Then use the rule to complete the table. m 0 15 30 40 50n 0 3 6Describe the relationship in words.

Answer 1

Let's use the data in the table as coordinates in getting its equation. We get Point A: (0,0) = x1,y1 and Point B: (15,3) = x2,y2.

Let's use the two points to get the equation. Applying the rules in getting the equation in Slope-Intercept Form.

Step 1: Let's determine the slope of the line (m).

$\text{ m = }\frac{y_2-y_1}{x_2-x_1}$$\text{ = }\frac{3\text{ - 0}}{15\text{ - 0}}\text{ = }\frac{3}{15}$$=\text{ }\frac{\frac{3}{3}}{\frac{15}{3}}$$\text{ m = }\frac{1}{5}$

Step 2: Let's determine the y-intercept (b). Substitute m = 1/5 and x,y = 0,0 in y = mx + b.

$\text{ y = mx + b}$$\text{ 0 = (}\frac{1}{5})(0)\text{ + b}$$\text{ b = 0}$

Step 3: Let's complete the equation. Subsitute m = 1/5 and b = 0 in y = mx + b.

$\text{ y = mx + b}$$\text{ y = (}\frac{1}{5})x\text{ + (0)}$$y\text{ = }\frac{1}{5}x$

Therefore, the equation the fits the pattern in the table is y = (1/5)x or y = x/5. W here y = n and x = m.

$\text{The value of m is 5 times the value of n.}$

Let's complete the table.

m solution n

0 0

15 3

30 6

40 = (1/5)(40) = 8 8

50 = (1/5)(50) = 10 10