Question

graph this line using the slope and y-intercept:
y = -4x + 9
click to select points on the graph.

Explanation:

Step1: Identify slope and y - intercept

The equation of the line is in the slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=-4x + 9\), the slope \(m=-4\) (which can be written as \(\frac{-4}{1}\)) and the y - intercept \(b = 9\). So, the y - intercept point is \((0,9)\) (since when \(x = 0\), \(y=9\)).

Step2: Plot the y - intercept

On the coordinate plane, find the point where \(x = 0\) and \(y = 9\). This is the point \((0,9)\) on the y - axis.

Step3: Use the slope to find another point

The slope \(m=\frac{\text{rise}}{\text{run}}=\frac{-4}{1}\). Starting from the y - intercept \((0,9)\), we move down 4 units (because the rise is - 4, which means a decrease of 4) and then move 1 unit to the right (because the run is 1). So, from \((0,9)\), moving down 4 gives \(y=9 - 4=5\) and moving right 1 gives \(x = 0+1 = 1\). So, the new point is \((1,5)\). We can also move up 4 units and left 1 unit (since \(\frac{-4}{1}=\frac{4}{-1}\)) from the y - intercept. Starting from \((0,9)\), moving up 4 gives \(y = 9+4 = 13\) (but this is outside the visible grid) and moving left 1 gives \(x=0 - 1=-1\), so the point \((-1,13)\) is also on the line but not visible. We can use the point \((1,5)\) (or other points found by the slope) to draw the line.

To graph the line, we first plot the y - intercept \((0,9)\) and then use the slope to find another point (like \((1,5)\)) and then draw a straight line through these points.

(Note: Since the problem is about graphing, the key points to plot are \((0,9)\) and another point like \((1,5)\) (or \((2,1)\), \((3, - 3)\) etc. by continuing to use the slope \(\frac{-4}{1}\)) to draw the line.)

Answer:

To graph \(y=-4x + 9\):

1. Plot the \(y\) - intercept at \((0,9)\) (on the \(y\) - axis, 9 units up from the origin).
2. Use the slope \(m=-4=\frac{-4}{1}\): From \((0,9)\), move down 4 units and right 1 unit to get the point \((1,5)\) (or other points by repeating the slope movement).
3. Draw a straight line through the plotted points (e.g., \((0,9)\) and \((1,5)\)) to represent the line \(y=-4x + 9\).