Question

1. slope = -2, through (-1, 5)

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. Here, $m=-2$, $x_1=-1$ and $y_1 = 5$.
Substitute these values into the point - slope form: $y - 5=-2(x - (-1))$, which simplifies to $y - 5=-2(x + 1)$.

Step2: Simplify the equation

Expand the right - hand side: $y-5=-2x-2$.
Then, add 5 to both sides of the equation to get the slope - intercept form $y=mx + b$. So, $y=-2x-2 + 5$, which simplifies to $y=-2x+3$.

Step3: Graph the line

1. Plot the point $(-1,5)$ on the coordinate plane.
2. Use the slope to find another point. The slope $m = - 2=\frac{\text{rise}}{\text{run}}=\frac{-2}{1}$. From the point $(-1,5)$, move down 2 units (because rise is - 2) and then move 1 unit to the right (because run is 1). This gives the point $(0,3)$. We can also move up 2 units and left 1 unit from $(-1,5)$ to get the point $(-2,7)$.
3. Draw a straight line through the plotted points.

Answer:

The equation of the line is $y = - 2x+3$ and the graph is drawn by plotting the point $(-1,5)$ and using the slope to find other points (e.g., $(0,3)$ or $(-2,7)$) and then drawing a line through them.