Question

graph this line using the slope and y-intercept:
y = -3x - 4
click to select points on the graph.
(graph with x-axis from -10 to 10 and y-axis from -10 to 10, grid lines, and axes arrows)

Explanation:

Step1: Identify y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=-3x - 4\), \(b=-4\). So the y - intercept is the point \((0,-4)\). We plot this point on the graph (the point where \(x = 0\) and \(y=-4\)).

Step2: Determine the slope

The slope \(m=-3\), which can be written as \(\frac{-3}{1}\) (or \(\frac{3}{-1}\)). The slope represents the change in \(y\) over the change in \(x\) (\(m=\frac{\Delta y}{\Delta x}\)). Starting from the y - intercept \((0,-4)\), using the slope \(\frac{\Delta y}{\Delta x}=\frac{-3}{1}\), we move 1 unit to the right (increase \(x\) by 1) and 3 units down (decrease \(y\) by 3). So from \((0,-4)\), moving 1 unit right to \(x = 1\) and 3 units down from \(y=-4\) gives us \(y=-4-3=-7\), so the point \((1,-7)\) is also on the line. We can also use the slope \(\frac{3}{-1}\): move 1 unit to the left (decrease \(x\) by 1) and 3 units up (increase \(y\) by 3). From \((0,-4)\), moving 1 unit left to \(x=-1\) and 3 units up gives \(y=-4 + 3=-1\), so the point \((-1,-1)\) is on the line.

Step3: Draw the line

After plotting the y - intercept \((0,-4)\) and at least one other point (like \((1,-7)\) or \((-1,-1)\)), we draw a straight line passing through these points.

Answer:

To graph \(y = - 3x-4\), plot the y - intercept \((0,-4)\) and use the slope \(-3\) to find another point (e.g., \((1,-7)\) or \((-1,-1)\)) and draw a line through them. The key points are \((0,-4)\) and other points determined by the slope.