Question

What is the slope intercept equation for (0, 2) and (5, 4)?

Answer 1

To find the slope-intercept equation (of the form \(y = mx + b\)) for the line that passes through the points \((0, 2)\) and \((5, 4)\), we need to determine the slope \(m\) and the y-intercept \(b\).

1. **Calculate the slope \(m\)**:
The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the points \((0, 2)\) and \((5, 4)\):
\[
m = \frac{4 - 2}{5 - 0} = \frac{2}{5}
\]

2. **Use one of the points to find the y-intercept \(b\)**:
Since the point \((0, 2)\) is on the y-axis, the y-intercept \(b\) is simply 2.

3. **Write the equation**:
Now that we have both the slope and the y-intercept, we can write the equation:
\[
y = \frac{2}{5}x + 2
\]

Therefore, the slope-intercept equation for the line that passes through the points \((0, 2)\) and \((5, 4)\) is:
\[
y = \frac{2}{5}x + 2
\]