To adjust the equation \( y = 2x - 12 \) so that the line passes through the points (4, 8) and (10, 11), we need to first find the slope of the line that goes through these two points.
The slope \( m \) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
With points (4, 8) and (10, 11):
\[ m = \frac{11 - 8}{10 - 4} = \frac{3}{6} = \frac{1}{2} \]
So, the slope of the line that passes through the points (4, 8) and (10, 11) is \( \frac{1}{2} \).
Next, we can use the point-slope form of a line equation, which is given by:
\[ y - y_1 = m(x - x_1) \]
Let's use point (4,8) as \( (x_1, y_1) \):
\[ y - 8 = \frac{1}{2}(x - 4) \]
Now, simplify this equation:
\[ y - 8 = \frac{1}{2}x - 2 \] \[ y = \frac{1}{2}x + 6 \]
So, the new equation of the line that passes through the points (4, 8) and (10, 11) is:
\[ y = \frac{1}{2}x + 6 \]
You can graph this line, and it will pass through both (4, 8) and (10, 11).