Question

2 graph the linear equation y = x - 2.

Explanation:

Step1: Identify the y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=x - 2\), the y - intercept \(b=- 2\). So, the line crosses the y - axis at the point \((0,-2)\).

Step2: Determine the slope

The slope \(m = 1\) (since the equation is \(y = 1x-2\)). The slope \(m=\frac{\text{rise}}{\text{run}}=\frac{1}{1}\). From the y - intercept \((0, - 2)\), we can find another point by moving up 1 unit and to the right 1 unit (because rise = 1 and run = 1). So, from \((0,-2)\), moving up 1 and right 1 gives the point \((1,-1)\). We can also find a point by moving down 1 unit and to the left 1 unit from the y - intercept: from \((0,-2)\), moving down 1 and left 1 gives \((- 1,-3)\).

Step3: Plot the points and draw the line

Plot the points \((0,-2)\), \((1,-1)\) (and/or \((-1,-3)\)) on the coordinate plane. Then, draw a straight line passing through these points.

Answer:

To graph \(y = x-2\), plot the y - intercept \((0,-2)\), use the slope \(m = 1\) to find another point (e.g., \((1,-1)\) or \((-1,-3)\)), and draw a straight line through the plotted points.