Question

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

Explanation:

Step1: Identify the slope and y - intercept

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

Step2: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. Since \(b = 2\), we plot the point \((0,2)\) on the coordinate plane.

Step3: Use the slope to find another point

The slope \(m=\frac{\text{rise}}{\text{run}}=\frac{1}{2}\). This means that from the point \((0,2)\), we can move up 1 unit (rise) and then move 2 units to the right (run) to get the next point. So, from \((0,2)\), moving up 1 and right 2 gives us the point \((0 + 2,2+1)=(2,3)\). We can also move down 1 unit and left 2 units from \((0,2)\) to get another point: \((0-2,2 - 1)=(-2,1)\).

Step4: Draw the line

Using a straightedge, draw a line that passes through the points we have plotted (e.g., \((0,2)\), \((2,3)\), \((-2,1)\)). This line represents the graph of the equation \(y=\frac{1}{2}x + 2\).

Answer:

The graph of \(y = \frac{1}{2}x+2\) is a straight line with a y - intercept at \((0,2)\) and a slope of \(\frac{1}{2}\), passing through points such as \((2,3)\) and \((-2,1)\) (or other points found using the slope from the y - intercept).