Question

How can you write the equation for a linear function if you know only two ordered pairs for the function?
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Answer 1

Answer:

Use the two ordered pairs to find the slope, m.

Then substitute one set of ordered pairs and m into y = mx + b to solve for b

Step-by-step explanation:

If we are given two ordered pairs of a function and we need to write an equation that represents the linear function, first, what we need to do is to use the two ordered pair to find the slope, m, using the formula, $m = \frac{y_2 - y_1}{x_2 - x_1}$.

After getting the slope (m), find the value of the y-intercept (b), by substituting the value of one of the ordered pairs and the slope value (m) into y = mx + b.

Once the value of m and b is known, plug in the value of m and b into y = mx + b to derive the equation of the linear function.

Answer 2

Use the 2 ordered pairs to find the slope, m .

Then substitute m and one set of ordered pairs into y = mx + b to solve for b.

If given the 2 ordered pairs for a function, the ordered pairs can be first used to find the slope of the function.

For example

(x₁, y₁)(x₂, y₂)

m = slope = y₂ - y₁ / x₂ - x₁

The slope(m) is then substituted in the slope intercept form equation.

y = mx + b

where

m = slope

b = y-intercept

And one set of the ordered pairs is also substituted in the equation to get the value of the y-intercept(b).

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