Question

What is the slope-intercept equation for the like below?
(0, 2) to (5, 4)

Answer 1

To find the slope-intercept equation (y = mx + b) of the line passing through the points (0, 2) and (5, 4), we need to calculate the slope (m) and the y-intercept (b).

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

Substitute the values into the formula:
\[
m = \frac{4 - 2}{5 - 0} = \frac{2}{5}
\]

2. **Determine the y-intercept (b):**
The y-intercept (b) is the value of y when x = 0. From the point (0, 2), we can see that b = 2.

3. **Write the equation in slope-intercept form:**
Now that we have both the slope (m = \(\frac{2}{5}\)) and the y-intercept (b = 2), we can write the equation of the line:
\[
y = \frac{2}{5}x + 2
\]

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