Question

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

Explanation:

Step1: Identify the type of function

The equation \( y = \frac{3}{2}x \) is a linear function in the form \( y = mx + b \), where \( m=\frac{3}{2} \) (slope) and \( b = 0 \) (y - intercept). So, the line passes through the origin \((0,0)\).

Step2: Find another point

To graph the line, we can use the slope. The slope \( m=\frac{3}{2} \) means for every 2 units we move to the right (increase in \( x \) by 2), we move up 3 units (increase in \( y \) by 3). Starting from the origin \((0,0)\), if we let \( x = 2 \), then \( y=\frac{3}{2}\times2=3 \). So, the point \((2,3)\) is also on the line.

Step3: Draw the line

Plot the points \((0,0)\) and \((2,3)\) on the coordinate grid and draw a straight line passing through these two points. The line should extend in both directions.

Answer:

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

1. Recognize it is a linear function with \( y \)-intercept \( (0,0) \) and slope \( \frac{3}{2} \).
2. Plot the point \( (0,0) \).
3. Use the slope: from \( (0,0) \), move 2 units right and 3 units up to plot \( (2,3) \).
4. Draw a straight line through \( (0,0) \) and \( (2,3) \), extending it in both directions.