Question

1. $y = \frac{2}{3}x - 2$

Explanation:

Step1: Identify the y - intercept

The equation of the line is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=\frac{2}{3}x - 2\), the y - intercept \(b=- 2\). This means the line crosses the y - axis at the point \((0,-2)\).

Step2: Use the slope to find another point

The slope \(m = \frac{2}{3}\), which can be interpreted as \(\frac{\text{rise}}{\text{run}}=\frac{2}{3}\). Starting from the y - intercept \((0,-2)\), we move up 2 units (rise) and then 3 units to the right (run). So, from \((0,-2)\), moving up 2 units gives \(y=-2 + 2=0\) and moving 3 units to the right gives \(x = 0+3 = 3\). So, we get the point \((3,0)\).

Step3: Plot the points and draw the line

First, plot the point \((0,-2)\) on the y - axis. Then, plot the point \((3,0)\) (since \(x = 3\) and \(y = 0\)). After that, draw a straight line passing through these two points. We can also find more points for accuracy. For example, if we take \(x=-3\), then \(y=\frac{2}{3}\times(-3)-2=-2 - 2=-4\), so the point \((-3,-4)\) is also on the line. Plot this point and draw the line through all the plotted points.

Answer:

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

1. Plot the y - intercept \((0,-2)\).
2. Use the slope \(\frac{2}{3}\) to find another point (e.g., from \((0,-2)\), move up 2, right 3 to get \((3,0)\)).
3. Draw a straight line through the plotted points.