Question

What is the y-intercept of this line

(Line goes from (0, 1) to (2, 7))

What is the equation of the libe

Answer 1

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 \(y = 3x + 1\).