Question

graph the line.
y = -3x - 2

Explanation:

Step1: Identify slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For \(y=-3x - 2\), the slope \(m=-3\) (or \(\frac{-3}{1}\)) and the y - intercept \(b = - 2\). So, the line crosses the y - axis at \((0,-2)\).

Step2: Plot the y - intercept

On the coordinate plane, find the point \((0,-2)\) (where \(x = 0\) and \(y=-2\)) and mark it.

Step3: Use the slope to find another point

The slope \(m=\frac{-3}{1}\) means from the y - intercept \((0,-2)\), we move down 3 units (because the numerator of the slope is - 3, which represents a change in \(y\)) and then move right 1 unit (because the denominator of the slope is 1, which represents a change in \(x\)). So, starting from \((0,-2)\), moving down 3 gives \(y=-2 - 3=-5\) and moving right 1 gives \(x = 0+1 = 1\). So, the new point is \((1,-5)\). We can also move up 3 and left 1 (since a negative slope can be thought of as \(\frac{3}{-1}\)). From \((0,-2)\), moving up 3 gives \(y=-2 + 3 = 1\) and moving left 1 gives \(x=0 - 1=-1\), so the point \((-1,1)\) is also on the line.

Step4: Draw the line

Connect the points \((0,-2)\), \((1,-5)\), \((-1,1)\) (or any two points found using the slope) with a straight line and extend it in both directions.

Answer:

To graph \(y = - 3x-2\), plot the y - intercept \((0,-2)\), then use the slope \(-3\) (rise - 3, run 1 or rise 3, run - 1) to find another point (e.g., \((1,-5)\) or \((-1,1)\)) and draw a straight line through the points.