Slope equation

To find the slope (m) of the line that goes from the point (0, 1) to the point (3, 7), we can use the slope formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Here, we can assign:

• \( (x_1, y_1) = (0, 1) \)
• \( (x_2, y_2) = (3, 7) \)

Now, substituting the values into the formula:

\[ m = \frac{7 - 1}{3 - 0} = \frac{6}{3} = 2 \]

So, the slope of the line is \( m = 2 \).

Next, to find the equation of the line, we can use the point-slope form of the equation of a line:

\[ y - y_1 = m(x - x_1) \]

Using the point \( (0, 1) \) and the slope \( m = 2 \):

\[ y - 1 = 2(x - 0) \]

Simplifying this gives:

\[ y - 1 = 2x \] \[ y = 2x + 1 \]

Therefore, the equation of the line is:

\[ y = 2x + 1 \]