what is the equation of the line that passes through the point (-1,6) and has a slope of 1?

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope.

Step2: Substitute values

Given $(x_1,y_1)=(-1,6)$ and $m = 1$. Substitute into the point - slope form: $y-6=1\times(x - (-1))$.

Step3: Simplify the equation

$y-6=x + 1$. Rearranging to slope - intercept form $y=x+7$.

Answer:

$y=x + 7$