Question

Write an equation that best describes the pattern in the table.

Answer 1

To be able to write the equation that best represents the pattern in the table, let's use at least two sets of the data that will serve as coordinates in getting the slope (m) and y-intercept (b) and use it to write the equation in Slope-Intercept Form: y = mx + b.

Let's get Point A: (0,0) = x1,y1 and Point B: (4,8) = x2,y2.

Step 1: Let's determine the Slope (m).

`\text{ m = }\frac{y_2-y_1_{}}{x_2-x_1}`
`\text{ = }\frac{8\text{ - 0}}{4\text{ - 0}}`
`\text{ m = }(8)/(4)\text{ = 2}`

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

`\text{ y = mx + b}`
`\text{ 0 = (2)(0) + b}`
`\text{ b = 0}`

Step 3: Let's complete the equation. Substitute m = 2 and b = 0 in y = mx + b.

`\text{ y = mx + b}`
`\text{ y = (2)x + (0)}`
`\text{ y = 2x}`

Therefore, the equation that best describes the pattern in the table is y = 2x.