Complete the slope-intercept form of the linear equation that represents the relationship in the table.
y = ___ x + ___
Complete the slope-intercept form of the linear equation that represents the relationship in the table.
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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