Question

1. slope = 0, through (4, -2)

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given that the slope $m = 0$, the equation of the line becomes $y=0\times x + b$, so $y = b$.

Step2: Find the value of $b$

The line passes through the point $(4,-2)$. Substitute $x = 4$ and $y=-2$ into the equation $y = b$. Since for any $x$, $y$ has the same value (because slope is 0, the line is horizontal), when $x = 4$, $y=-2$, so $b=-2$. The equation of the line is $y=-2$.

Step3: Graph the line

To graph the line $y = - 2$, we know that it is a horizontal line. A horizontal line with $y=-2$ will pass through all points where the $y$ - coordinate is - 2. In the given coordinate grid, we find the point $(4,-2)$ and then draw a horizontal line (parallel to the $x$ - axis) passing through this point and all other points with $y=-2$.

Answer:

The line is a horizontal line $y=-2$ passing through $(4, - 2)$ (graphically, a horizontal line at $y=-2$ on the coordinate grid).