Question

graph the line containing the point p and having slope m.
p = (-5, -7); m = 0

use the graphing tool to graph the line.
click to enlarge graph

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 $m = 0$, the equation of the line becomes $y=0\times x + b=y = b$.

Step2: Find the value of b

We know that the line passes through the point $P=(-5,-7)$. Substitute $x=-5$ and $y = - 7$ into the equation $y=b$. Since when $x=-5$, $y=-7$, and the equation is $y = b$, we have $b=-7$. So the equation of the line is $y=-7$.

Step3: Analyze the graph of $y = - 7$

The line $y=-7$ is a horizontal line. A horizontal line has a slope of 0 (which matches the given slope $m = 0$). For a horizontal line $y = k$ (in this case $k=-7$), all the points on the line have a y - coordinate of $k$. So the line passes through $(-5,-7)$ and any other point with $y=-7$, for example, $(0,-7),(1,-7),(-1,-7)$ etc. To graph the line, we can plot the point $(-5,-7)$ and then draw a horizontal line (parallel to the x - axis) through this point.

Answer:

The equation of the line is $y=-7$, and it is a horizontal line passing through the point $(-5,-7)$ (and all other points with $y - coordinate=-7$). To graph it, plot the point $(-5,-7)$ and draw a horizontal line (parallel to the x - axis) through this point.