Question

graph the line with slope -1 passing through the point (-4, -2).

Explanation:

Step1: Recall the point - slope form

The point - slope form of a line 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, $m=- 1$, $x_1=-4$ and $y_1 = - 2$. Substituting these values into the point - slope form, we get $y-(-2)=-1(x - (-4))$, which simplifies to $y + 2=-1(x + 4)$.

Step2: Simplify the equation

Expand the right - hand side: $y+2=-x - 4$. Then, solve for $y$: $y=-x-4 - 2=-x - 6$.

Step3: Plot the given point

First, locate the point $(-4,-2)$ on the coordinate plane. The $x$-coordinate is - 4 (4 units to the left of the origin on the $x$-axis) and the $y$-coordinate is - 2 (2 units below the origin on the $y$-axis).

Step4: Use the slope to find another point

The slope $m=-1=\frac{\text{rise}}{\text{run}}=\frac{-1}{1}$. From the point $(-4,-2)$, if we move 1 unit to the right (increase $x$ by 1, run = 1) and 1 unit down (decrease $y$ by 1, rise=-1), we get the point $(-4 + 1,-2-1)=(-3,-3)$. If we move 1 unit to the left (decrease $x$ by 1) and 1 unit up (increase $y$ by 1), we get the point $(-4-1,-2 + 1)=(-5,-1)$.

Step5: Draw the line

Draw a straight line passing through the points $(-4,-2)$, $(-3,-3)$ and $(-5,-1)$ (or other points found using the slope) and extend it in both directions.

(Note: Since the problem is about graphing, the final answer is the graph of the line $y=-x - 6$ passing through $(-4,-2)$ with a slope of - 1. If we were to describe the key points: The line passes through $(-4,-2)$, $(-3,-3)$, $(-5,-1)$, $(0,-6)$, $( - 6,0)$ etc. and has a negative slope, going from the second quadrant to the fourth quadrant.)

Answer:

The graph of the line with slope - 1 passing through $(-4,-2)$ is a straight line with equation $y=-x - 6$ passing through the point $(-4,-2)$ and other points determined by the slope (e.g., $(-3,-3)$, $(-5,-1)$ etc.)