Question

47 graph the following equation. y = x - 2

Explanation:

Step1: Identify the equation type

The equation \( y = x - 2 \) is in slope - intercept form \( y=mx + b \), where \( m = 1 \) (slope) and \( b=- 2 \) (y - intercept).

Step2: Find the y - intercept

The y - intercept is the point where \( x = 0 \). Substitute \( x = 0 \) into the equation: \( y=0 - 2=-2 \). So the point \( (0,-2) \) is on the line.

Step3: Use the slope to find another point

The slope \( m = 1=\frac{1}{1} \), which means for every 1 unit we move to the right (increase in \( x \) by 1), we move up 1 unit (increase in \( y \) by 1). From the point \( (0,-2) \), if we move \( x = 0+1 = 1 \), then \( y=-2 + 1=-1 \). So the point \( (1,-1) \) is also on the line.

Step4: Plot the points and draw the line

Plot the points \( (0,-2) \) and \( (1,-1) \) on the coordinate grid. Then draw a straight line passing through these two points (and extending in both directions) since the equation represents a linear function.

Answer:

To graph \( y=x - 2 \), plot the y - intercept \( (0,-2) \) and use the slope \( m = 1 \) to find another point (e.g., \( (1,-1) \)), then draw a straight line through these points. The graph is a straight line with a slope of 1 and y - intercept at \( (0,-2) \).