Question

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

Explanation:

Step1: Find the equation of the line

We use the point - slope formula $y - y_1=m(x - x_1)$ to find the equation of the line. Substituting $m = 1,x_1=-2,y_1=-4$ gives $y+4=x + 2$, which simplifies to $y=x - 2$.

Step2: Graph the line

We start by plotting the given point $(-2,-4)$. Then, using the slope of 1 (rise over run = 1/1), we find additional points and draw a straight line through them.

Answer:

1. First, use the point - slope form of a line: $y - y_1=m(x - x_1)$. Given $m = 1$, $x_1=-2$ and $y_1=-4$.

• Substitute the values into the formula: $y-(-4)=1\times(x - (-2))$.
• Simplify to get $y + 4=x + 2$.
• Then rewrite it in slope - intercept form $y=x - 2$.

1. To graph the line:

• Plot the given point $(-2,-4)$ on the coordinate plane.
• Since the slope $m = 1=\frac{1}{1}$, from the point $(-2,-4)$, move 1 unit to the right and 1 unit up to get another point. We can also move 1 unit to the left and 1 unit down.
• Connect the points with a straight line.