Question

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 given by $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.
We are given that the point $(x_1,y_1)=(- 1,6)$ and the slope $m = 1$.

Step2: Substitute values into point - slope form

Substitute $x_1=-1$, $y_1 = 6$ and $m = 1$ into the point - slope formula:
$y-6=1\times(x - (-1))$
Simplify the right - hand side: $y - 6=x + 1$

Step3: Convert to slope - intercept form (optional, but to get a more standard form)

Add 6 to both sides of the equation:
$y=x + 1+6$
$y=x+7$
We can also write it in the general form $x - y+7 = 0$, but the slope - intercept form $y=x + 7$ is also correct.

Answer:

The equation of the line is $y=x + 7$ (or $x - y+7 = 0$)