Question

what is the equation of the line that passes through the point (-1, 1) and has a slope of 5?

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.
Here, $x_1=- 1$, $y_1 = 1$ and $m = 5$.

Step2: Substitute values into point - slope form

Substitute $x_1=-1$, $y_1 = 1$ and $m = 5$ into the point - slope formula:
$y-1 = 5(x-(-1))$
Simplify the right - hand side: $y - 1=5(x + 1)$

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

Expand the right - hand side: $y-1=5x + 5$
Add 1 to both sides of the equation: $y=5x+5 + 1$
So, $y = 5x+6$

We can also write it in standard form $Ax+By = C$. Starting from $y=5x + 6$, subtract $y$ and 6 from both sides: $5x-y=-6$

Answer:

The equation of the line is $y = 5x+6$ (or $5x - y=-6$)