Question

What is the slope-intercept equation for the line below?

(4, 3) to (0, 1)

Answer 1

To find the slope-intercept form of the equation of a line given two points, we need to calculate the slope (m) and the y-intercept (b).

**Step 1: Calculate the slope (m)**

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

For the points (4, 3) and (0, 1):
- \( (x_1, y_1) = (4, 3) \)
- \( (x_2, y_2) = (0, 1) \)

Plugging in these values:

\[
m = \frac{1 - 3}{0 - 4} = \frac{-2}{-4} = \frac{1}{2}
\]

**Step 2: Find the y-intercept (b)**

Now that we have the slope, we can use one of the points to find the y-intercept \( b \). We'll use the point (0, 1), which is already in the y-intercept format (0, b).

Here, the y-intercept \( b = 1 \).

**Step 3: Write the equation in slope-intercept form**

The slope-intercept form of a line is given by:

\[
y = mx + b
\]

Substituting \( m \) and \( b \):

\[
y = \frac{1}{2}x + 1
\]

Thus, the slope-intercept equation for the line through the points (4, 3) and (0, 1) is:

\[
y = \frac{1}{2}x + 1
\]