Question

For some real numder A the graph of theline y+=(A+1)x +8 in the stander (x,y) coordinate plane passes through (2,6) what the slope of this line

Answer 1

To find the slope of the line given by the equation \( y = (A + 1)x + 8 \) and that passes through the point \( (2, 6) \), we need to first substitute the coordinates of the point into the equation.

1. Plug \( x = 2 \) and \( y = 6 \) into the line equation:
\[
6 = (A + 1) \cdot 2 + 8
\]

2. Simplify the equation:
\[
6 = 2(A + 1) + 8
\]
\[
6 = 2A + 2 + 8
\]
\[
6 = 2A + 10
\]

3. Rearranging the equation to find \( A \):
\[
6 - 10 = 2A
\]
\[
-4 = 2A
\]
\[
A = -2
\]

4. Now substitute \( A \) back into the slope formula:
The slope (\( m \)) of the line is given by \( m = A + 1 = -2 + 1 = -1 \).

Therefore, the slope of the line is \(\boxed{-1}\).