Question

Identify the slope and the y-intercept if the line passes through (2, 11) and (6, 3)


Slope (m) =
y-intercept (b) =

Answer 1

To find the slope (m) of the line that passes through the points \((2, 11)\) and \((6, 3)\), we can use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

Here, \((x_1, y_1) = (2, 11)\) and \((x_2, y_2) = (6, 3)\). Plugging in these values:

\[
m = \frac{3 - 11}{6 - 2} = \frac{-8}{4} = -2
\]

Now that we have the slope, we can find the y-intercept (b) by using the slope-intercept form of the equation of a line, which is given by:

\[
y = mx + b
\]

We can use one of the points to solve for \(b\). Let's use the point \((2, 11)\):

\[
11 = -2(2) + b
\]
\[
11 = -4 + b
\]
\[
b = 11 + 4 = 15
\]

Now we have both the slope and the y-intercept:

- Slope (m) = -2
- y-intercept (b) = 15

Thus, the final answers are:

Slope (m) = -2
y-intercept (b) = 15