Final answer:
The slope-intercept equation for the new line is y = 2x - 6.
Step-by-step explanation:
The slope-intercept form of a linear equation is of the form y = mx + b, where m represents the slope and b represents the y-intercept. In the given equation, y = 2x - 8, the slope is 2 and the y-intercept is -8.
When a graph is translated by a vector [a, b], the equation of the new line can be obtained by adding a to the x-values and b to the y-values in the original equation. So, if we translate the line y = 2x - 8 by the vector [1, 1], the equation of the new line would be y = 2(x + 1) - 8.
Simplifying the equation, we get y = 2x - 6. Therefore, the slope-intercept equation for the new line is y = 2x - 6.