Question

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

Explanation:

Step1: Identify the slope-intercept form

The equation is given 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 slope \(m=\frac{2}{3}\) and the y - intercept \(b=- 2\).

Step2: Plot the y - intercept

The y - intercept \(b = - 2\) means the line crosses the y - axis at the point \((0,-2)\). Locate the point \((0,-2)\) on the coordinate plane.

Step3: Use the slope to find another point

The slope \(m=\frac{2}{3}\) can be thought of as \(\frac{\text{rise}}{\text{run}}\), where rise is the change in \(y\) and run is the change in \(x\). So, from the point \((0,-2)\), we move up 2 units (because the numerator of the slope is 2) and then move to the right 3 units (because the denominator of the slope is 3). This gives us the point \((0 + 3,-2+2)=(3,0)\).

Step4: Draw the line

Draw a straight line that passes through the points \((0,-2)\) and \((3,0)\) (and extends in both directions).

(If the question was to graph the line \(y = \frac{2}{3}x-2\), the graph should pass through \((0, - 2)\) and \((3,0)\) with a slope of \(\frac{2}{3}\))

Answer:

The line \(y=\frac{2}{3}x - 2\) is graphed by plotting the y - intercept \((0,-2)\) and then using the slope \(\frac{2}{3}\) to find another point \((3,0)\) and drawing a line through these points.