Question

Write the equation of the line that is graphed. Use Slope-Intercept Form, y = mx +b.
the ponits are (2,6) and (0,3)

Answer 1

To find the equation of the line in Slope-Intercept Form (y = mx + b) using the points (2, 6) and (0, 3), follow these steps:

1. **Determine the slope (m):**
The slope formula is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (x₁, y₁) = (0, 3) and (x₂, y₂) = (2, 6):
\[
m = \frac{6 - 3}{2 - 0} = \frac{3}{2}
\]

2. **Use the slope (m) and one point to find the y-intercept (b):**
We can use the point (0, 3), which is the y-intercept (where x = 0). In Slope-Intercept Form, b is the y-coordinate of this point.
Thus, \( b = 3 \).

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

Therefore, the equation of the line is:
\[
\boxed{y = \frac{3}{2}x + 3}
\]