Question

given the equation; y = -2/3x + 4 graph the line.

Explanation:

Step1: Identify the 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 \(y=-\frac{2}{3}x + 4\), the slope \(m =-\frac{2}{3}\) and the y - intercept \(b = 4\). This means the line crosses the y - axis at the point \((0,4)\).

Step2: Plot the y - intercept

On the coordinate plane, find the point \((0,4)\) and mark it.

Step3: Use the slope to find another point

The slope \(m=-\frac{2}{3}=\frac{\text{rise}}{\text{run}}\). The rise is \(- 2\) (which means we go down 2 units) and the run is \(3\) (which means we go to the right 3 units) from the y - intercept \((0,4)\). So, starting from \((0,4)\), moving down 2 units and right 3 units gives us the point \((0 + 3,4-2)=(3,2)\). We can also use the rise of \(2\) (up 2 units) and run of \(-3\) (left 3 units) from \((0,4)\) to get the point \((0-3,4 + 2)=(-3,6)\).

Step4: Draw the line

Connect the points (such as \((0,4)\), \((3,2)\), \((-3,6)\)) with a straight line. The given graph in the problem seems to be incorrect for the equation \(y =-\frac{2}{3}x+4\) as the slope of the line in the graph appears to be positive (since it is increasing from left to right), but the slope of our equation is negative. The correct line should be decreasing from left to right.

Answer:

To graph \(y =-\frac{2}{3}x + 4\):

1. Plot the y - intercept \((0,4)\).
2. Use the slope \(-\frac{2}{3}\) to find additional points (e.g., \((3,2)\) or \((-3,6)\)).
3. Draw a straight line through the plotted points. The line should have a negative slope (decreasing from left to right), unlike the positively - sloped line in the provided graph.