Question

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

Explanation:

Step1: Identify the slope-intercept form

The equation \( y = \frac{3}{2}x - \frac{1}{2} \) is in slope - intercept form \( y=mx + b \), where \( m=\frac{3}{2} \) (slope) and \( b =-\frac{1}{2} \) (y - intercept).

Step2: Find the y - intercept

The y - intercept \( b=-\frac{1}{2} \), so the line crosses the y - axis at the point \( (0,-\frac{1}{2}) \).

Step3: Use the slope to find another point

The slope \( m = \frac{3}{2}=\frac{\text{rise}}{\text{run}} \). From the y - intercept \( (0,-\frac{1}{2}) \), we can go up 3 units and then right 2 units.

• Starting at \( (0,-\frac{1}{2}) \), moving up 3 units: \( y=-\frac{1}{2}+ 3=\frac{- 1 + 6}{2}=\frac{5}{2} \)
• Moving right 2 units: \( x = 0+2 = 2 \)

So we get the point \( (2,\frac{5}{2})=(2,2.5) \). We can also verify by plugging \( x = 1 \) into the equation: \( y=\frac{3}{2}(1)-\frac{1}{2}=\frac{3 - 1}{2}=1 \), so the point \( (1,1) \) is also on the line.

Step4: Draw the line

Plot the points \( (0,-\frac{1}{2}) \), \( (1,1) \), \( (2,2.5) \) etc. and draw a straight line through them.

Answer:

To graph \( y=\frac{3}{2}x-\frac{1}{2} \):

1. Plot the y - intercept at \( (0,-\frac{1}{2}) \).
2. Use the slope \( \frac{3}{2} \) to find additional points (e.g., from \( (0,-\frac{1}{2}) \), move up 3, right 2 to get \( (2,2.5) \) or plug in \( x = 1 \) to get \( (1,1) \)).
3. Draw a straight line through the plotted points.