To find the slope (m) and y-intercept (b) of the line that passes through the points (2, 11) and (6, 3), we can follow these steps:
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:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (2, 11) and (6, 3):
- \(x_1 = 2\), \(y_1 = 11\)
- \(x_2 = 6\), \(y_2 = 3\)
Plugging the values into the formula:
\[
m = \frac{3 - 11}{6 - 2} = \frac{-8}{4} = -2
\]
Step 2: Find the Y-Intercept (b)
To find the y-intercept (b), we can use the slope-intercept form of the equation of a line, which is:
\[
y = mx + b
\]
We can choose one of the points and the slope to solve for \(b\). Let's use the point (2, 11):
\[
11 = -2(2) + b
\]
This simplifies to:
\[
11 = -4 + b
\]
\[
b = 11 + 4 = 15
\]
Summary
So, we have:
- Slope (m) = -2
- Y-intercept (b) = 15