Question

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

Explanation:

Step1: Identify the slope and y-intercept

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

Step2: Plot the y-intercept

The y - intercept is \( - 3 \), so we plot the point \( (0,-3) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( \frac{1}{2} \) means "rise over run", or \( \frac{\text{change in }y}{\text{change in }x} \). From the point \( (0,-3) \), we rise (move up) 1 unit and run (move right) 2 units. This gives us the point \( (0 + 2,-3+1)=(2,-2) \). We can also go in the opposite direction: from \( (0,-3) \), rise - 1 (move down 1) and run - 2 (move left 2) to get the point \( (0-2,-3 - 1)=(-2,-4) \).

Step4: Draw the line

Draw a straight line through the points we have plotted (such as \( (0,-3) \), \( (2,-2) \), \( (-2,-4) \)). This line represents the graph of the equation \( y=\frac{1}{2}x - 3 \).

Answer:

The graph of \( y = \frac{1}{2}x-3 \) is a straight line with a y - intercept at \( (0,-3) \) and a slope of \( \frac{1}{2} \), passing through points like \( (2,-2) \) and \( (-2,-4) \) (among others) when plotted on the coordinate plane.