To find the equation of a linear function that passes through two points, we need the coordinates of those points.
Let's say the linear function passes through the points \((0, b)\) and \((1, m)\). Here \(b\) is the y-intercept (the value of the function when \(x = 0\)) and \(m\) is the value of the function when \(x = 1\).
The general form of a linear function is given by the equation:
\[ y = mx + b \]
where \(m\) is the slope of the line and \(b\) is the y-intercept.
To find the slope \(m\), we can use the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \((0, b)\) and \((1, m)\), we have:
- \((x_1, y_1) = (0, b)\)
- \((x_2, y_2) = (1, m)\)
Substituting these values into the slope formula gives:
\[ m = \frac{m - b}{1 - 0} = m - b \]
Thus, the slope of the linear function can also be expressed as:
\[ y = (m - b)x + b \]
This is the general representation of the linear function that passes through the specified points. If you provide the actual values for \(b\) and \(m\), I can substitute them into this equation to give you the specific function.