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 = }(y_2-y_1)/(x_2-x_1)`
`\text{ = }\frac{3\text{ - 0}}{15\text{ - 0}}\text{ = }(3)/(15)`
`=\text{ }((3)/(3))/((15)/(3))`
`\text{ m = }(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 = (}(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 = (}(1)/(5))x\text{ + (0)}`
`y\text{ = }(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