Question

graph the line.
$y = -3x - 3$

Explanation:

Step1: Identify the y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=-3x - 3\), \(b=-3\). So the line crosses the y - axis at the point \((0,-3)\).

Step2: Identify the slope

The slope \(m=-3\), which can be written as \(\frac{-3}{1}\) (rise over run). From the y - intercept \((0,-3)\), we can find another point by moving down 3 units (because the rise is - 3) and 1 unit to the right (run is 1). So starting from \((0,-3)\), moving down 3 and right 1 gives the point \((1,-6)\). We can also find a point by moving up 3 units and left 1 unit from the y - intercept: \((0 - 1,-3 + 3)=(-1,0)\).

Step3: Plot the points and draw the line

Plot the points \((0,-3)\) and \((-1,0)\) (or \((1,-6)\)) on the coordinate plane. Then draw a straight line passing through these points.

(Note: Since the problem is about graphing, the final answer is the visual representation of the line \(y = - 3x-3\) passing through the points \((0,-3)\) and \((-1,0)\) (or other points found using the slope - intercept method) on the given grid.)

Answer:

The line \(y=-3x - 3\) is graphed by plotting the y - intercept \((0,-3)\) and using the slope \(-3\) to find another point (e.g., \((-1,0)\) or \((1,-6)\)) and then drawing a straight line through these points.