Question

What is the slope-intercept equation for the line below?
(5, 4)
(0, 2) •
Equation is
Answer
y=-5/2x + 2
My =-2/5x+2
:: y= 5/2x + 2
:: y= 2/5x + 2

Answer 1

To find the slope-intercept equation of the line that passes through the points (5, 4) and (0, 2), we need to determine the slope (m) and the y-intercept (b). The slope-intercept form of a line is given by the equation:

\[ y = mx + b \]

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

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

Using the points (5, 4) and (0, 2):

- Let \((x_1, y_1) = (0, 2)\) and \((x_2, y_2) = (5, 4)\).
- Then:

\[
m = \frac{4 - 2}{5 - 0} = \frac{2}{5}
\]

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

3. **Write the slope-intercept equation:**
Now that we have the slope and the y-intercept, we can write the equation of the line:

\[
y = \frac{2}{5}x + 2
\]

So, the correct slope-intercept equation for the line is:

\[
\boxed{y = \frac{2}{5}x + 2}
\]