Complete the slope-intercept form of the linear equation that represents the relationship in the table.

To find the slope-intercept form of a linear equation (y = mx + b) from a table, you will need to determine two key components:

1. Slope (m): The slope is calculated by taking the difference in y-values divided by the difference in x-values between two points from the table. Choose two points (x₁, y₁) and (x₂, y₂) and use the formula:

[

m = frac{y₂ – y₁}{x₂ – x₁}

]

2. Y-Intercept (b): Once you have the slope, you can substitute one of the points and the slope into the equation to find the y-intercept. You can rearrange the equation to solve for b:

[

b = y – mx

]

Let’s say you have the points (2, 3) and (4, 7) from the table:

– Calculate the slope:

[

m = frac{7 – 3}{4 – 2} = frac{4}{2} = 2

]

– Now, substitute in one of the points to find b. Using the point (2, 3):

[

3 = 2(2) + b implies 3 = 4 + b implies b = 3 – 4 = -1