Question

graph this line using the slope and y-intercept:
y = -6x + 5
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 \(y=-6x + 5\), \(b = 5\). So the y - intercept is the point \((0,5)\). Plot this point on the graph (where \(x = 0\) and \(y=5\)).

Step2: Use slope to find next point

The slope \(m=-6\), which can be written as \(\frac{-6}{1}\) (rise over run). From the y - intercept \((0,5)\), we move down 6 units (because the rise is - 6) and right 1 unit (because the run is 1). So the new point is \((0 + 1,5-6)=(1,-1)\). We can also move up 6 units and left 1 unit from \((0,5)\) to get \((0 - 1,5 + 6)=(-1,11)\) (but \((-1,11)\) may be outside the visible grid, so \((1,-1)\) is more practical for graphing here).

Step3: Draw the line

After plotting the y - intercept \((0,5)\) and the point \((1,-1)\) (or other points found using the slope), draw a straight line through these points to represent the equation \(y=-6x + 5\).

Answer:

To graph \(y=-6x + 5\):

1. Plot the y - intercept \((0,5)\) (since when \(x = 0\), \(y=5\)).
2. Use the slope \(m=-6=\frac{-6}{1}\): from \((0,5)\), move down 6 units and right 1 unit to get \((1,-1)\), or up 6 units and left 1 unit to get \((-1,11)\).
3. Draw a straight line through the plotted points.