Question

graph this line using the slope and y-intercept: y = -5x - 5 click to select points on the graph.

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 \(y=-5x - 5\), the slope \(m=-5=\frac{- 5}{1}\) and the y - intercept \(b = - 5\). So the line crosses the y - axis at the point \((0,-5)\).

Step2: Use slope to find another point

The slope is \(\frac{\text{rise}}{\text{run}}=\frac{-5}{1}\). Starting from the y - intercept \((0,-5)\), we move down 5 units (because the rise is - 5) and 1 unit to the right (because the run is 1). So we get the point \((0 + 1,-5-5)=(1,-10)\). We can also move up 5 units and 1 unit to the left. Starting from \((0,-5)\), moving up 5 units (\(y=-5 + 5=0\)) and left 1 unit (\(x = 0-1=-1\)) gives the point \((-1,0)\).

Step3: Plot the points and draw the line

Plot the points \((0,-5)\) (on the y - axis, 5 units below the origin) and \((-1,0)\) (on the x - axis, 1 unit to the left of the origin) or \((1,-10)\) (if we use the first method of moving down and right). Then draw a straight line through these points.

Answer:

To graph \(y=-5x - 5\):

1. Plot the y - intercept: The point \((0,-5)\) (since when \(x = 0\), \(y=-5\)).
2. Use the slope \(-5=\frac{-5}{1}\): From \((0,-5)\), move 1 unit to the right and 5 units down to get the point \((1,-10)\), or 1 unit to the left and 5 units up to get the point \((-1,0)\).
3. Draw a straight line through the plotted points.