What is the y-intercept of this line

To find the equation of the line that goes through the points \((0, 1)\) and \((2, 7)\), we can start by calculating the slope \(m\) of the line using the formula:

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

Using the points \((0, 1) \equiv (x_1, y_1)\) and \((2, 7) \equiv (x_2, y_2)\):

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

Now that we have the slope \(m = 3\), we can use the point-slope form of the line equation:

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

Using \((0, 1)\) as our point \((x_1, y_1)\):

\[ y - 1 = 3(x - 0) \]

Simplifying this gives:

\[ y - 1 = 3x \] \[ y = 3x + 1 \]

The y-intercept is the value of \(y\) when \(x = 0\). From the equation \(y = 3x + 1\), we can see that the y-intercept is \(1\).

Final Results:

• The y-intercept is \(1\).
• The equation of the line is \(y = 3x + 1\).