Question

What is the y-intercept of this line?
10-
(2,7)
(0,1) •
一
-10
10
-10 -
y-intercept =
type your answer...
What is the equation of the line? choose your answer...

Answer 1

To find the y-intercept of the line that passes through the points (2, 7) and (0, 1), we can use the fact that the y-intercept is the value of \(y\) when \(x = 0\).

From the coordinates provided, we see directly that the point (0, 1) corresponds to the y-intercept. Thus:

**Y-intercept = 1**

Next, to find the equation of the line, we can calculate the slope \(m\) of the line using the two points (2, 7) and (0, 1):

1. **Calculate the slope (\(m\)):**
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 1}{2 - 0} = \frac{6}{2} = 3
\]

2. **Use the point-slope form of the line equation:**
The point-slope form is given by:
\[
y - y_1 = m(x - x_1)
\]
Using the point (0, 1) and the slope \(m = 3\):
\[
y - 1 = 3(x - 0)
\]
\[
y - 1 = 3x
\]
\[
y = 3x + 1
\]

**Equation of the line: \(y = 3x + 1\)**

To summarize:
- **Y-intercept = 1**
- **Equation of the line: \(y = 3x + 1\)**